The 22^{nd} term of the arithmetic sequence where a_{1} = 8 and a_{9} = 56 is **134**.

Contents

- 1 What is the 24th term of the arithmetic sequence where a1 8 and a9 56?
- 2 What is the 24th term of the arithmetic sequence where a1 8 and a9 56 134 140 146 152?
- 3 How do you find the 21st term of an arithmetic sequence?
- 4 What is the 24th term?
- 5 What is the 7th term of the geometric sequence where a1 − 4096 and a4 64?
- 6 What is the 7th term of the geometric sequence where a1 1024 and a4 − 16?
- 7 What is the thirty second term?
- 8 What is the sum of the terms of the arithmetic sequence 34 39 44 49?
- 9 What is the arithmetic mean between 10 and 24?
- 10 How do you find the 15th term?
- 11 How do you find the 25th term in a sequence?
- 12 What is the 22nd te…
- 13 What Is The 22Nd Term Of The Arithmetic Sequence Where A1 = 8 And A9 = 56
- 14 Frequently Asked Question:
- 14.1 What is the 17th term in the arithmetic sequence?
- 14.2 What is the 19th term of the sequence?
- 14.3 What is the 25th term of the arithmetic sequence 3 7 11 15?
- 14.4 What is the next term of the arithmetic sequence 14 20 26?
- 14.5 What is the formula of the sum of arithmetic sequence?
- 14.6 How can you find the sum of the terms of the arithmetic sequence if the number of terms n is unknown?
- 14.7 What is the 25th term of arithmetic sequence?
- 14.8 What is the sum of the arithmetic sequence 8 14 20 If there are 24 terms?
- 14.9 What is the sum of the arithmetic sequence 8 14 20 If there are 24 terms?
- 14.10 What is the formula of the sum of arithmetic sequence?

- 15 What Is The 24Th Term Of The Arithmetic Sequence Where A1 = 8 And A9 = 56?
- 16 Frequently Asked Question:
- 16.1 What is the formula for the sum of an arithmetic sequence?
- 16.2 How can you find the sum of the terms of the arithmetic sequence if the number of terms n is unknown?
- 16.3 What is the sum of the terms in a sequence?
- 16.4 What is the 23rd term of the arithmetic sequence where a1 8 and a9 48?
- 16.5 What is the sum of the arithmetic sequence 8 14 20 If there are 24 terms 6 points?
- 16.6 What is the 24th term?
- 16.7 What are terms in a sequence?
- 16.8 What is the 18th term of the arithmetic sequence?
- 16.9 What is 18th term of the sequence where a1 3 and D 7?
- 16.10 What are the terms of an arithmetic sequence?
- 16.11 What is a term in math?
- 16.12 What is the formula for the sum of an arithmetic sequence?
- 16.13 How can you find the sum of the terms of the arithmetic sequence if the number of terms n is unknown?
- 16.14 What is the sum of the terms in a sequence?

- 17 What is the 22nd term of the arithmetic sequence where a1 8 and a9 56 6 points?
- 17.1 What is the 24th term of the arithmetic sequence where a1 8 and a9 56?
- 17.2 What is the 23rd term of the arithmetic sequence where a1 8 and a9 48 6 points?
- 17.3 What is the sum of the arithmetic sequence 6/14 22 If there are 26 terms 6 points?
- 17.4 What is the 25 th term?
- 17.5 What is the sum of the arithmetic sequence 8 14 20 If there are 24 terms?
- 17.6 What is the 25th term in the arithmetic sequence 2 5 8?
- 17.7 How to find the n th term of an arithmetic sequence?
- 17.8 How to find the sum of the first 40 terms of the sequence?
- 17.9 How to find the rule of the sequence?
- 17.10 What do you call a sequence of numbers?
- 17.11 What is the 23rd term of the arithmetic sequence?
- 17.12 What is the 22nd term of the arithmetic sequence where a1 8 and a9 56?
- 17.13 What is the 32nd term of the arithmetic sequence where a1 =- 33?
- 17.14 What is the 24th term of the arithmetic sequence when a1 8?
- 17.15 How do you find the 32nd term of a sequence?
- 17.16 What is the 24th term of the arithmetic sequence?
- 17.17 Which is the 24th term of the arithmetic sequence?
- 17.18 When do you use an arithmetic sequence calculator?
- 17.19 Which is the formula for the nth term of an arithmetic sequence?
- 17.20 What do you call a sequence of numbers?

- 18 What is the 22nd term of the arithmetic sequence where a1 = 8 and a9 = 56 ?
- 19 Arithmetic Sequences and Series
- 20 Arithmetic Series

## What is the 24th term of the arithmetic sequence where a1 8 and a9 56?

The 24th term of the arithmetic sequence where a_{1} = 8 and a_{9} = 56 is 146.

## What is the 24th term of the arithmetic sequence where a1 8 and a9 56 134 140 146 152?

Thus, the 24th term is 146.

## How do you find the 21st term of an arithmetic sequence?

The formula for the nth term of an arithmetic sequence is the following: a (n) = a_{1} + (n-1) *d where d is the common difference, a_{1} is the first term, and n is the sequence term. In this case, d = 4, a_{1} = 8.

## What is the 24th term?

The 24th term is a24= 148.

## What is the 7th term of the geometric sequence where a1 − 4096 and a4 64?

What is the 7th term of the geometric sequence where a_{1} = -4,096 and a_{4} = 64? Summary: The 7th term of the geometric sequence where a_{1} = -4,096 and a_{4} = 64 is -1.

## What is the 7th term of the geometric sequence where a1 1024 and a4 − 16?

Summary: Given a_{1} = 1,024 and a_{4} = -16 the value of the 7th term of the geometric series is 1/4.

## What is the thirty second term?

2: the quotient of a unit divided by 32: one of 32 equal parts of anything one thirty-second of the total.

## What is the sum of the terms of the arithmetic sequence 34 39 44 49?

Therefore, you answer is 700.

## What is the arithmetic mean between 10 and 24?

Using the average formula, get the arithmetic mean of 10 and 24. Thus, 10+24/2 =17 is the arithmetic mean.

## How do you find the 15th term?

$n^{th}$ term of an A.P. is given by $a_n= a+(n-1)d$. In order to determine the 15th term of the given arithmetic sequence, we relate the given numbers with the general sequence of A.P. and Using the $n^{th}$ term formula, we find the 15th term in the given A.P.

## How do you find the 25th term in a sequence?

Solution: A sequence in which the difference between all pairs of consecutive numbers is equal is called an arithmetic progression. The sequence given is 3, 9, 15, 21, 27, … Therefore, the 25th term is 147.

## What is the 22nd te…

Free of charge, you may ask your own question! Mathematics OpenStudy (anonymous): What is the 22nd term of the arithmetic sequence in which a1 = 8 and a9 = 56 is derived from? Join the QuestionCove group and learn while studying with your classmates! To enroll, call 134142150158 or open a study (anonymous): 134142150158. Anonymous OpenStudy participants include: @campbell st @ranga Answers from OpenStudy (anonymous): a22= 134, a41=-145. OpenStudy (campbell st): well, the formula is as follows: you’ll need this to figure out what the common denominator is.

So 56 Equals 16 according to OpenStudy (anonymous) (d) How do you obtain d if you divide both sides?

Fill out the formOpenStudy (campbell st):well you have56 = 8 + 8dsbuttract 8 from both sides of the equation 48 x 8d = 48 x 8d now, find the value of d Study (anonymous): d=6 OpenStudy OpenStudy (campbell st):Yes, you are correct, and you now must As a result, according to OpenStudy (anonymous), a(n)=a1+(n1)d a22=8+(221)d 6 a22 = 8 + 126 a22 = 134 6 a22 = 8 + 126 a22 = 134 Campbell st (OpenStudy): excellent work.

Join the QuestionCove group and learn while studying with your classmates!

- @campbell st Seriously, I had no idea what I was talking about when it came to equations until I got your guidance on this one.
- OpenStudy (campbell st): I’m delighted to be of assistance.
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## What Is The 22Nd Term Of The Arithmetic Sequence Where A1 = 8 And A9 = 56

The answer is 134, which is the 22nd term in the arithmetic series. 30th of July, 2016 One answer to the question “What is the 24th term of the arithmetic sequence where a1 8 and a9 56?” As a result, the twenty-fourth period is 146. What is the 23rd term of the arithmetic sequence consisting of the numbers a1 8 and a9 48, in addition?, Answer:The 23rd term of A.P is 118. The following is a step-by-step explanation: In light of the fact that the first and ninth terms of the arithmetic sequence are the numbers 8 and 48, respectively.

The sum of the arithmetic sequences 8, 14, 20,., up to and including 24 terms equals S n= 1848 if there are 24 terms in total.

## Frequently Asked Question:

Ans: B: The arithmetic sequence contains the number 31/4 as the 103rd term.

### What is the 17th term in the arithmetic sequence?

In the arithmetic series, 31/4 is the 103rd term, which is denoted by B.

### What is the 19th term of the sequence?

The numbers in the given sequence are 7, 13, 19, 25,. As a result, the 115th term of the progression is the 19th term.

### What is the 25th term of the arithmetic sequence 3 7 11 15?

Answer: The 25th term in the sequence 3, 7, 11, 15, and 19 is a number called 99.

### What is the next term of the arithmetic sequence 14 20 26?

Answer. It is the 38th term that is coming up. The following term must be the fifth term.

### What is the formula of the sum of arithmetic sequence?

In an arithmetic series, the sum of the first n terms is equal to (n/2)(a1+a2). The arithmetic series formula is the name given to this formula.

### How can you find the sum of the terms of the arithmetic sequence if the number of terms n is unknown?

In an arithmetic series, the sum of the first n terms is equal to (n/2)(a1+an) Arithmetic series formula is what it’s called.

### What is the 25th term of arithmetic sequence?

There are two possible responses. Expert Tutors provide assistance. This is accomplished by the use of the equation (Y2-Y1)/ (X2-X1). … An easier way to think about this equation is as follows: Y = 4X – 9 is a mathematical formula. To discover the twenty-fifth phrase, just substitute 25 for X. Y = 4(25) – 9, which results in the 25th end of this sequence91.

### What is the sum of the arithmetic sequence 8 14 20 If there are 24 terms?

The sum of the arithmetic sequences 8, 14, 20,., up to and including 24 terms is S n= 1848.

### What is the sum of the arithmetic sequence 8 14 20 If there are 24 terms?

To find out how many terms there are in an arithmetic series of 8, 14, 20,., up to 24, use the formula S n= 1848.

### What is the formula of the sum of arithmetic sequence?

In an arithmetic series, the sum of the first n terms is equal to (n/2)(a1+a2). The arithmetic series formula is the name given to this formula. (It has been visited 1 time, with 1 visit today)

## What Is The 24Th Term Of The Arithmetic Sequence Where A1 = 8 And A9 = 56?

There is just one answer. As a result, the twenty-fourth period is 146. The 9th of May, 2016 What is the twenty-fourth term in the sequence?, and The twenty-fourth term is a24=148. As an example of this, what is the 22nd term of the algebraic series in which a1 8 and A9 56?, and what is the 22nd term of the arithmetic sequence in which The answer is 134, which is the 22nd term in the arithmetic series. Last but not least, what is the total of the mathematical sequence 8 14 20? If there are 24 words, how many points are there?

Let’s see if we can figure out the total of the above arithmetic series.

## Frequently Asked Question:

- Figure out what the common difference is, d
- A n = a 1 + d (n 1). Substitute the common difference and the first term into an=a1+d(n1) to get an=a1+d(n1). Solve for n by substituting the final term with an.

### What is the formula for the sum of an arithmetic sequence?

When n words in anarithmetic sequence are added together, the result is (n/2)(a1+an). The formula for thearithmetic series is referred to as thearithmetic series formula.

### How can you find the sum of the terms of the arithmetic sequence if the number of terms n is unknown?

We can calculate the sum of the terms in the arithmetic sequence by discovering the unknown numbers of terms (n) and using the nth formula of the arithmetic sequencean=a1+(n -1)d, and we can also find the common difference (d) if necessary. We can also find the common difference (d) if necessary.

### What is the sum of the terms in a sequence?

Aseries are the total of all the terms in a sequence of events.

### What is the 23rd term of the arithmetic sequence where a1 8 and a9 48?

Answer: The number 118 represents the 23rd term of A.P. The following is a step-by-step explanation: In light of the fact that the first and ninth terms of the arithmetic sequence are the numbers 8 and 48, respectively.

### What is the sum of the arithmetic sequence 8 14 20 If there are 24 terms 6 points?

The sum of the arithmetic sequences 8, 14, 20,., up to and including 24 terms is S n= 1848. Let’s see if we can figure out the total of the above arithmetic series.

### What is the 24th term?

The twenty-fourth term is a24=148.

### What are terms in a sequence?

A sequence is a set of numbers that are presented in a certain order.

Each integer in a series is referred to as an aterm. Each phrase in a series has a corresponding place (first, second, third and so on). To illustrate, take the following example: Each number in this sequence is referred to as aterm.

### What is the 18th term of the arithmetic sequence?

142 is the number of the 18th term. The total of the first 18 words is 1332.

### What is 18th term of the sequence where a1 3 and D 7?

It is sufficient to utilize the first formula to determine the nthterm. As a result, the 122nd term is the 18th term.

### What are the terms of an arithmetic sequence?

This type of sequence exists when you pick any number from the series and subtract it by its preceding number, and the outcome is always the same or constant. So the words in this series are created in this manner: If the average difference between successive phrases is positive, we may argue that the frequency of these terms is growing.

### What is a term in math?

Atermis a mathematical expression that is a single word. It might be a single number (positive or negative), a single variable (a letter), many variables multiplied but never added or subtracted, or numerous variables multiplied but never combined. Several words contain variables that are denoted by a number before them.

### What is the formula for the sum of an arithmetic sequence?

When n words in anarithmetic sequence are added together, the result is (n/2)(a1+an). The formula for thearithmetic series is referred to as thearithmetic series formula.

### How can you find the sum of the terms of the arithmetic sequence if the number of terms n is unknown?

We can calculate the sum of the terms in the arithmetic sequence by discovering the unknown numbers of terms (n) and using the nth formula of the arithmetic sequencean=a1+(n -1)d, and we can also find the common difference (d) if necessary. We can also find the common difference (d) if necessary.

### What is the sum of the terms in a sequence?

Aseries are the total of all the terms in a sequence of events. (It has been visited 1 time, with 1 visit today)

## What is the 22nd term of the arithmetic sequence where a1 8 and a9 56 6 points?

The answer is 134, which is the 22nd term in the arithmetic series.

### What is the 24th term of the arithmetic sequence where a1 8 and a9 56?

As a result, the 24th term is 146.

### What is the 23rd term of the arithmetic sequence where a1 8 and a9 48 6 points?

The answer is 118, which is the 23rd term in the arithmetic series.

### What is the sum of the arithmetic sequence 6/14 22 If there are 26 terms 6 points?

Assume that there are 26 terms in the arithmetic sequence 6, 14, 22, and you get a total of 2755.6

### What is the 25 th term?

To obtain the 25th term, just substitute 25 for X.Y =4(25) – 9, which results in the 25th term in this series being number 91.

### What is the sum of the arithmetic sequence 8 14 20 If there are 24 terms?

1848 n = 1848 is the total of the arithmetic sequences 8, 14, 20,., up to a maximum of 24 terms in the sequence.

### What is the 25th term in the arithmetic sequence 2 5 8?

As a result, the 25th term is 74.

### How to find the n th term of an arithmetic sequence?

An Arithmetic Sequence’s nth term is represented by the following formula: In an arithmetic series, the formula for the n th term is a = (a1 + (n – 1))x (d). Where n denotes the word number

### How to find the sum of the first 40 terms of the sequence?

The sum of the first 40 terms in the arithmetic sequence 2, 5, 8, 11, is equal to the number 40. To begin, locate the 40th term: The answer is 40 since 1 + (n – 1) d = 2 + 39 (3) = 119.

### How to find the rule of the sequence?

In order to determine the rule of the sequence from the sequence, we must label the terms of the sequence with the term numbers that appear in the sequence (values of n). The common difference (d) between the two words is to be found. Calculate the difference (d) by multiplying it by the variable n, which gives us the result “dn”.

### What do you call a sequence of numbers?

What Is the Arithmetic Sequence and How Does It Work?

An arithmetic sequence, also known as an arithmetic progression, is a sequence of integers in which the difference between any two succeeding members of the sequence is a constant. An arithmetic series is a collection of components of a finite arithmetic progression that are added together.

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As a result, the 23rd word in the series is 118.

### What is the 23rd term of the arithmetic sequence?

As a result, a = 11 and d = 3, resulting in 23 = 11 + 3. (23-1) 3. The 23rd term is 77 since 11 + 22(3) = 77 = [11 + 22(3) = 77 =]

### What is the 22nd term of the arithmetic sequence where a1 8 and a9 56?

The answer is 134, which is the 22nd term in the arithmetic series.

### What is the 32nd term of the arithmetic sequence where a1 =- 33?

As a result, the 32nd term is 374. I hope this has been of assistance!

### What is the 24th term of the arithmetic sequence when a1 8?

As a result, the 24th term is 146.

### How do you find the 32nd term of a sequence?

This results in 146 being the twenty-fourth term.

### What is the 24th term of the arithmetic sequence?

The twenty-fourth period is a 24=148.

### Which is the 24th term of the arithmetic sequence?

How many terms are there in the arithmetic sequence where a1 = 8 and a9 = 56? The following graph depicts the sequence a = 1 (3)n n 1: Calculate the average rate of change between n = 1 and n = 3 throughout the period of time. Which of the following sequences is represented by the graph below?

### When do you use an arithmetic sequence calculator?

This Arithmetic Sequence Calculator is used to compute the nth term of an arithmetic series as well as the sum of the first n terms of the sequence. What Is the Arithmetic Sequence and How Does It Work?

### Which is the formula for the nth term of an arithmetic sequence?

It is possible to calculate the nth term of an arithmetic series using the formula An = a + (n – 1)d, where a denotes the first word, n the term number, and d is the difference between the terms.

### What do you call a sequence of numbers?

What Is the Arithmetic Sequence and How Does It Work? An arithmetic sequence, also known as an arithmetic progression, is a sequence of integers in which the difference between any two succeeding members of the sequence is a constant. An arithmetic series is a collection of components of a finite arithmetic progression that are added together.

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When considering an arithmetic series, the first term is, and the fifth term is. What is the second slang phrase? The correct response is:Explanation: The formula may be used to determine the common difference. Isandis is the name we use. We now have a problem to solve. The second term is obtained by multiplying the first term by the common difference. When you add up the first three terms of an arithmetic series, you get 111; the sum of the fourth term gets you 49. What is the first term? Answers that might be given include: It is unable to make a determination based on the facts provided.

- The first three words are as follows, in no particular order: The sum of the first three terms equals the following.
- The fourth term is equal to the second term multiplied by twice the average difference: It is possible to solve for the common difference by using the second and fourth terms’ values of 37 and 49, respectively.
- The first of these terms is.
- Find the 31st phrase in the series if is the initial term in the sequence.
- The correct solution is: What is the first phrase in the sentence?
- What is the length of its first term?
- In an arithmetic series with a first term and common difference, the ninth term is equal to 87.

What is the length of its first term?

In order to determine the common difference, we must remove the tenth and eighth terms from each other and solve for: Now, put the eighth termequal to 87, set it, and solve it as follows: The 100th term in the arithmetic series that follows must be found.

Please keep in mind that the basic rule for this sequence iswhere represents the first number in the sequence,is the common difference between subsequent numbers, andis the tenth number in the sequence.

Another point to note is that every time we move up from one number to another, the number rises by 7.

The following is how the rule for this sequence is written: Now that we’ve discovered our rule, we can proceed to figure out what the 100th term is equivalent to by applying it.

The correct response is: Explanation: Begin by determining the common difference between the first and second terms in this sequence, which may be obtained by subtracting the first term from the second term.

To solve for the 26th term in the following arithmetic sequence, use the following formula: The correct response is: Explanation: Starting with the first term, subtract the second term from the first to discover the common difference between the two terms.

What is the eleventh phrase in the sequence below, given the information provided?

are the numbers one through five.

The difference between each gap is 4, hence the 11th term would be supplied by 10 * 4 + 1 = 41.

The first of these terms is 1. Each subsequent term rises by a factor of four. The n thterm will be equal to 1 + (n – 1) where n is the number of terms (4). The eleventh term will be 1 + (11 – 1)(4)1 + (10)(4)1 + (10)(4)1 + (40)(4) = 1 + (40) = 41.

## What is the 22nd term of the arithmetic sequence where a1 = 8 and a9 = 56 ?

When considering an arithmetic series, the first term is and the fifth term is What is the second slang expression? Reason for the correct response: The formula may be used to find the common difference. isandis means a lot to us. Fortunately, we now have a solution! The second term is obtained by adding the common difference to the first term. The sum of the first three terms in an arithmetic series is 111, while the sum of the fourth term is 49, as shown in the diagram. What is the first phrase in the sentence?

- Reason for the correct response: Let’s call it the common difference, and let’s call it the second term, respectively.
- The sum of the first three terms equals the following: Our second term will be 37 years from today.
- The most often encountered difference is six (see below).
- The 31st phrase must be found if and only if is the first word in the series.
- Let us use the common difference in the series as an example of a correct answer: Otherwise, or in a similar manner, or in a similar manner Arithmetic sequences have nine terms, with the ninth and tenth terms being represented by the numbers 87 and 99.

Reason for the correct response: The difference between the tenth and ninth words is the most common difference in the sequence: To solve an arithmetic sequence with first term and common difference, we set the ninth term to 87, set, and then answer the following equation: Arithmetic sequences have 87 and 99 as the eighth and tenth terms, respectively.

- Obtaining the correct response: An explanation: The eighth and tenth terms of the series are and, where is the first term and is the common difference between them.
- Obtaining the correct response: Explanation: We must first discover a rule for this arithmetic series in order to figure out the 100th term.
- As a result of our issue, Aside from that, every time we move up from one number to another, the number increases by seven.
- This is how we write down the rule for this sequence: Following the discovery of our rule, we may proceed to determine what the 100th term equals.
- Thus Any term in an arithmetic sequence may be found by using the following formula: The first term is, is the number of terms to discover, and is the common difference between the first and second terms in the series Find the 18th term in the arithmetic series that follows.
- Obtaining the correct response: Explanation: Begin by determining the common difference between the first and second terms in this series, which may be obtained by subtracting the first term from the second term in this sequence.
- Obtaining the correct response: Explanation: Beginning with the first term, subtract the second term from the first to discover the common difference between the two terms.
- What is the eleventh term of the series, given the information in the following?
- are the numbers one through five.
- The 11th term would be supplied by 10 * 4 + 1 = 41, because each gap has a difference of +4.

First and foremost, the phrase 1 means “first.” Following then, the phrase lengthens by a factor of 4. There will be a n thterm equal to 1 + (n – 1), which will be equal to 1. (4). The eleventh term will be 1 + (11 – 1)(4)1 + (10)(4)1 + (10)(4)1 + (40)(4) = 1 + (40) = 41

## Arithmetic Sequences and Series

The succession of arithmetic operations There is a series of integers in which each subsequent number is equal to the sum of the preceding number and specified constants. orarithmetic progression is a type of progression in which numbers are added together. This term is used to describe a series of integers in which each subsequent number is the sum of the preceding number and a certain number of constants (e.g., 1). an=an−1+d Sequence of Arithmetic Operations Furthermore, becauseanan1=d, the constant is referred to as the common difference.

For example, the series of positive odd integers is an arithmetic sequence, consisting of the numbers 1, 3, 5, 7, 9, and so on.

This word may be constructed using the generic terman=an1+2where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, where, To formulate the following equation in general terms, given the initial terma1of an arithmetic series and its common differenced, we may write: a2=a1+da3=a2+d=(a1+d)+d=a1+2da4=a3+d=(a1+2d)+d=a1+3da5=a4+d=(a1+3d)+d=a1+4d⋮ As a result, we can see that each arithmetic sequence may be expressed as follows in terms of its initial element, common difference, and index: an=a1+(n−1)d Sequence of Arithmetic Operations In fact, every generic word that is linear defines an arithmetic sequence in its simplest definition.

### Example 1

Identify the general term of the above arithmetic sequence and use that equation to determine the series’s 100th term. For example: 7,10,13,16,19,… Solution: The first step is to determine the common difference, which is d=10 7=3. It is important to note that the difference between any two consecutive phrases is three. The series is, in fact, an arithmetic progression, with a1=7 and d=3. an=a1+(n1)d=7+(n1)3=7+3n3=3n+4 and an=a1+(n1)d=7+(n1)3=7+3n3=3n+4 and an=a1+(n1)d=3 As a result, we may express the general terman=3n+4 as an equation.

To determine the 100th term, use the following equation: a100=3(100)+4=304 Answer_an=3n+4;a100=304 It is possible that the common difference of an arithmetic series be negative.

### Example 2

Identify the general term of the given arithmetic sequence and use it to determine the 75th term of the series: 6,4,2,0,−2,… Solution: Make a start by determining the common difference, d = 4 6=2. Next, determine the formula for the general term, wherea1=6andd=2 are the variables. an=a1+(n−1)d=6+(n−1)⋅(−2)=6−2n+2=8−2n As a result, an=8nand the 75thterm may be determined as follows: an=8nand the 75thterm a75=8−2(75)=8−150=−142 Answer_an=8−2n;a100=−142 The terms in an arithmetic sequence that occur between two provided terms are referred to as arithmetic means.

The terms of an arithmetic sequence that occur between two supplied terms.

### Example 3

Find all of the words that fall between a1=8 and a7=10. in the context of an arithmetic series Or, to put it another way, locate all of the arithmetic means between the 1st and 7th terms. Solution: Begin by identifying the points of commonality. In this situation, we are provided with the first and seventh terms, respectively: an=a1+(n−1) d Make use of n=7.a7=a1+(71)da7=a1+6da7=a1+6d Substitutea1=−8anda7=10 into the preceding equation, and then solve for the common differenced result. 10=−8+6d18=6d3=d Following that, utilize the first terma1=8.

a1=3(1)−11=3−11=−8a2=3 (2)−11=6−11=−5a3=3 (3)−11=9−11=−2a4=3 (4)−11=12−11=1a5=3 (5)−11=15−11=4a6=3 (6)−11=18−11=7} In arithmetic, a7=3(7)11=21=10 means a7=3(7)11=10 Answer: 5, 2, 1, 4, 7, and 8.

### Example 4

Find the general term of an arithmetic series with a3=1 and a10=48 as the first and last terms. Solution: We’ll need a1 and d in order to come up with a formula for the general term. Using the information provided, it is possible to construct a linear system using these variables as variables. andan=a1+(n−1) d:{a3=a1+(3−1)da10=a1+(10−1)d⇒ {−1=a1+2d48=a1+9d Make use of a3=1. Make use of a10=48. Multiplying the first equation by one and adding the result to the second equation will eliminate a1.

an=a1+(n−1)d=−15+(n−1)⋅7=−15+7n−7=−22+7n Answer_an=7n−22 Take a look at this!

For example: 32,2,52,3,72,… Answer_an=12n+1;a100=51

## Arithmetic Series

Series of mathematical operations When an arithmetic sequence is added together, the result is called the sum of its terms (or the sum of its terms and numbers). Consider the following sequence: S5=n=15(2n1)=++++= 1+3+5+7+9+25=25, where S5=n=15(2n1)=++++ = 1+3+5+7+9=25, where S5=n=15(2n1)=++++= 1+3+5+7+9 = 25. Adding 5 positive odd numbers together, like we have done previously, is manageable and straightforward. Consider, on the other hand, adding the first 100 positive odd numbers. This would be quite time-consuming.

When we write this series in reverse, we get Sn=an+(and)+(an2d)+.+a1 as a result.

2.:Sn=n(a1+an) 2 Calculate the sum of the first 100 terms of the sequence defined byan=2n1 by using this formula. There are two variables, a1 and a100. The sum of the two variables, S100, is 100 (1 + 100)2 = 100(1 + 199)2.

### Example 5

The sum of the first 50 terms of the following sequence: 4, 9, 14, 19, 24,. is to be found. The solution is to determine whether or not there is a common difference between the concepts that have been provided. d=9−4=5 It is important to note that the difference between any two consecutive phrases is 5. The series is, in fact, an arithmetic progression, and we may writean=a1+(n1)d=4+(n1)5=4+5n5=5n1 as an anagram of the sequence. As a result, the broad phrase isan=5n1 is used. For this sequence, we need the 1st and 50th terms to compute the 50thpartial sum of the series: a1=4a50=5(50)−1=249 Then, using the formula, find the partial sum of the given arithmetic sequence that is 50th in length.

### Example 6

Evaluate:Σn=135(10−4n). This problem asks us to find the sum of the first 35 terms of an arithmetic series with a general terman=104n. The solution is as follows: This may be used to determine the 1 stand for the 35th period. a1=10−4(1)=6a35=10−4(35)=−130 Then, using the formula, find out what the 35th partial sum will be. Sn=n(a1+an)2S35=35⋅(a1+a35)2=352=35(−124)2=−2,170 2,170 is the answer.

### Example 7

In an outdoor amphitheater, the first row of seating comprises 26 seats, the second row contains 28 seats, the third row contains 30 seats, and so on and so forth. Is there a maximum capacity for seating in the theater if there are 18 rows of seats? The Roman Theater (Fig. 9.2) (Wikipedia) Solution: To begin, discover a formula that may be used to calculate the number of seats in each given row. In this case, the number of seats in each row is organized into a sequence: 26,28,30,… It is important to note that the difference between any two consecutive words is 2.

where a1=26 and d=2.

As a result, the number of seats in each row may be calculated using the formulaan=2n+24.

In order to do this, we require the following 18 thterms: a1=26a18=2(18)+24=60 This may be used to calculate the 18th partial sum, which is calculated as follows: Sn=n(a1+an)2S18=18⋅(a1+a18)2=18(26+60) 2=9(86)=774 There are a total of 774 seats available.

Calculate the sum of the first 60 terms of the following sequence of numbers: 5, 0, 5, 10, 15,.

Answer:S60=−8,550

### Key Takeaways

- When the difference between successive terms is constant, a series is called an arithmetic sequence. According to the following formula, the general term of an arithmetic series may be represented as the sum of its initial term, common differenced term, and indexnumber, as follows: an=a1+(n−1)d
- An arithmetic series is the sum of the terms of an arithmetic sequence
- An arithmetic sequence is the sum of the terms of an arithmetic series
- As a result, the partial sum of an arithmetic series may be computed using the first and final terms in the following manner: Sn=n(a1+an)2

### Topic Exercises

- Given the first term and common difference of an arithmetic series, write the first five terms of the sequence. Find a formula that describes the generic term. The values of a1 are 5 and 3
- 12 and 2
- 15 and 5
- 7 and 4 respectively
- 12 and 1
- A1=23 and 13 respectively
- 1 and 12 respectively
- A1=54 and 14. The values of a1 are 1.8 and 0.6
- 4.3 and 2.1
- And a1=5.4 and 2.1 respectively.

- Locate a formula for the general term and apply it to get the 100 thterm, given the arithmetic series given the sequence 0.8, 2, 3.2, 4.4, 5.6,.
- 4.4, 7.5, 13.7, 16.8,.
- 3, 8, 13, 18, 23,.
- 3, 7, 11, 15, 19,.
- 6, 14, 22, 30, 38,.
- 5, 10, 15, 20, 25,.
- 2, 4, 6, 8, 10,.
- 12,52,92,132,.
- 13, 23, 53,83,.
- 14,12,54,2,114,. Find the positive odd integer that is 50th
- Find the positive even integer that is 50th
- Find the 40 th term in the sequence that consists of every other positive odd integer in the following format: 1, 5, 9, 13,.
- Find the 40th term in the sequence that consists of every other positive even integer: 1, 5, 9, 13,.
- Find the 40th term in the sequence that consists of every other positive even integer: 2, 6, 10, 14,.
- 2, 6, 10, 14,. What number is the term 355 in the arithmetic sequence 15, 5, 5, 15, 25,.
- What number is the phrase 172 in the arithmetic sequence 4, 4, 12, 20, 28,.
- What number is the term 355 in the arithmetic sequence 15, 5, 5, 15, 25,.
- Find an equation that yields the general term in terms of a1 and the common differenced given the arithmetic sequence described by the recurrence relationan=an1+5wherea1=2 andn1 and the common differenced
- Find an equation that yields the general term in terms ofa1and the common differenced, given the arithmetic sequence described by the recurrence relationan=an1-9wherea1=4 andn1
- This is the problem.

- Find a formula for the general term from the terms of an arithmetic sequence given the terms of the series. 1 = 6 and 7 = 42
- 1 = 12 and 12= 6
- 1 = 19 and 26 = 56
- 1 = 9 and 31 = 141
- 1 = 16 and 10 = 376
- 1 = 54 and 11 = 654. 1 = 6 and 7 = 42
- 1= 9 and 31 = 141
- 1 = 6 and 7

- Find all of the arithmetic means that exist between the two supplied terms. a1=3anda6=17
- A1=5anda5=7
- A2=4anda8=7
- A5=12anda9=72
- A5=15anda7=21
- A6=4anda11=1

### Part B: Arithmetic Series

- In light of the general term’s formula, figure out how much the suggested total is. an=3n+5
- S100
- An=5n11
- An=12n
- S70
- An=132n
- S120
- An=12n34
- S20
- An=n35
- S150
- An=455n
- S65
- An=2n48
- S95
- An=4.41.6n
- S75
- An=6.5n3.3
- S67
- An=3n+5

- Evaluate. 1160(3n)
- 1121(2n)
- 1250(4n-3)
- 1120(2n+12)
- 170 (198n)
- 1220(5n)
- 160(5212n)
- 151(38+14
- 1120(1.5n+2.6)
- 1175(0.2N1.6)
- 1170 (19 The total of all 200 positive integers is found by counting them up. To solve this problem, find the sum of the first 400 positive integers.

- The generic term for a sequence of positive odd integers is denoted byan=2n1 and is defined as follows: Furthermore, the generic phrase for a sequence of positive even integers is denoted by the number an=2n. Look for the following. The sum of the first 50 positive odd numbers
- The sum of the first 200 positive odd integers
- The sum of the first 500 positive odd integers
- The sum of the first 50 positive even numbers
- The sum of the first 200 positive even integers
- The sum of the first 500 positive even integers
- The sum of the firstk positive odd integers
- The sum of the firstk positive odd integers the sum of the firstk positive even integers
- The sum of the firstk positive odd integers
- There are eight seats in the front row of a tiny theater, which is the standard configuration. Following that, each row contains three additional seats than the one before it. How many total seats are there in the theater if there are 12 rows of seats? In an outdoor amphitheater, the first row of seating comprises 42 seats, the second row contains 44 seats, the third row contains 46 seats, and so on and so forth. When there are 22 rows, how many people can fit in the theater’s entire seating capacity? The number of bricks in a triangle stack are as follows: 37 bricks on the bottom row, 34 bricks on the second row and so on, ending with one brick on the top row. What is the total number of bricks in the stack
- Each succeeding row of a triangle stack of bricks contains one fewer brick, until there is just one brick remaining on the top of the stack. Given a total of 210 bricks in the stack, how many rows does the stack have? A wage contract with a 10-year term pays $65,000 in the first year, with a $3,200 raise for each consecutive year after. Calculate the entire salary obligation over a ten-year period (see Figure 1). In accordance with the hour, a clock tower knocks its bell a specified number of times. The clock strikes once at one o’clock, twice at two o’clock, and so on until twelve o’clock. A day’s worth of time is represented by the number of times the clock tower’s bell rings.

### Part C: Discussion Board

- Is the Fibonacci sequence an arithmetic series or a geometric sequence? How to explain: Using the formula for the then th partial sum of an arithmetic sequenceSn=n(a1+an)2and the formula for the general terman=a1+(n1)dto derive a new formula for the then th partial sum of an arithmetic sequenceSn=n2, we can derive the formula for the then th partial sum of an arithmetic sequenceSn=n2. How would this formula be beneficial in the given situation? Explain with the use of an example of your own creation
- Discuss strategies for computing sums in situations when the index does not begin with one. For example, n=1535(3n+4)=1,659
- N=1535(3n+4)=1,659
- Carl Friedrich Gauss is the subject of a well-known tale about his misbehaving in school. As a punishment, his instructor assigned him the chore of adding the first 100 integers to his list of disciplinary actions. According to folklore, young Gauss replied accurately within seconds of being asked. The question is, what is the solution, and how do you believe he was able to come up with the figure so quickly?

### Answers

- An=3n+2
- An=5n+3
- An=6n
- An=3n+2
- An=6n+3
- An=6n+2

- 1,565,450, 2,500,450, k2,
- 90,800, k4,230,
- 38640, 124,750,
- 18,550, k765
- 10,578
- 20,100,
- 2,500,550, k2,
- 294 seats, 247 bricks, $794,000, and so on.