**1 Answer**

- Given: arithmetic sequence: a10=100;a20=50.
- a10=a1+d⋅(10−1)=100. a10=a1+9d=100.
- a20=a1+d⋅(20−1)=50. a20=a1+19d=50.
- Equation 1: a1+9d=100. Equation 2 *(-1) = +−a1−19d=−50−−−−−−−−−−−−−−−−−−− −10d=50.
- d=−5.
- Find a1 by substitution: a1+19⋅−5=50.
- Simplify: a1−95=50.
- a1=50+95=145.

•

Contents

- 1 How do you find a number in an arithmetic sequence?
- 2 What is the arithmetic mean between 10 and 24?
- 3 What is the 10th term in the sequence?
- 4 Is 121 a term of this arithmetic sequence?
- 5 What is the arithmetic mean between 10 and 2?
- 6 What is the arithmetic mean of 4 and 9?
- 7 What is the 10th term of the given sequence an 3n 5?
- 8 How do you find 10 terms?
- 9 How do you find 10% of a number?
- 10 How to find the nth term of an arithmetic sequence – Algebra 1
- 11 SOLUTION: Hello, my name is kevin i need help with this 2 questions; Write an equation from the nth term of the architmetic sequence. Then find a10. 15. -2,5,12,19. 16. 13,9,5,1. P
- 12 Arithmetic Sequences and Series
- 13 Arithmetic Series
- 14 Let a1,a2,.a10 be an arithmetic sequence. If a1+a3+a5+a7+a9=17 and a2+a4+a6+a8+a10=15
- 15 Solve 100,110,120,130 Tiger Algebra Solver
- 16 Arithmetic sequences calculator that shows work
- 17 About this calculator

## How do you find a number in an arithmetic sequence?

Solution: To find a specific term of an arithmetic sequence, we use the formula for finding the nth term. Step 1: The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

## 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.

## What is the 10th term in the sequence?

The sequence of numbers – 2,5,8 and 11 form an AP whose first term is 2 and the common difference is 3. So the 10th term will be, T10 = a +(n-1)d = 2 + (10–1)*3 = 29.

## Is 121 a term of this arithmetic sequence?

121 is not a term in the sequence.

## What is the arithmetic mean between 10 and 2?

(10 — 2) = 8. d = (8 / 4) = 2. The arithmetic means are: 4, 6, 8.

## What is the arithmetic mean of 4 and 9?

What is the geometric mean of 4 and 9? The geometric mean of 4 and 9 is 6.

## What is the 10th term of the given sequence an 3n 5?

Oct 1, 2015. If an=3n−5. then. a10= 25.

## How do you find 10 terms?

How to find the nth term. To find the nth term, first calculate the common difference, d. Next multiply each term number of the sequence (n = 1, 2, 3, …) by the common difference. Then add or subtract a number from the new sequence to achieve a copy of the sequence given in the question.

## How do you find 10% of a number?

To find one tenth of a number, simply divide it by 10.

## How to find the nth term of an arithmetic sequence – Algebra 1

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 phrase in the sentence?

The correct response is:Explanation: Let us consider the common distinction, and let us consider the second term.

We now know that the second period is 37 days long.

The most often encountered difference is 6.

- The first character in an arithmetic sequence is.
- The fourth and tenth terms of an arithmetic series are 372 and 888, respectively.
- Let us consider the common difference in the series as our correct answer:Explanation: Then, alternatively, or equivalently, or alternatively, The ninth and tenth terms of an arithmetic series have the numbers 87 and 99, respectively, in their corresponding positions.
- The correct response is:Explanation: It is the difference between the tenth and ninth phrases in the sequence that is the most prevalent difference:.
- We put this equal to 87, and then proceed to solve: There are two terms in an arithmetic series that are the eighth and tenth terms, respectively: 87 and 99.
- The correct response is: An explanation: The eighth and tenth terms of the series are and, where is the first term and is the common difference between the two terms.
- The correct response is: Explanation: We must first discover a rule for this arithmetic series in order to be able to calculate the 100th term.
- This is the crux of the matter.
- Therefore,.

For the hundredth and last time, Thus To find any term in an arithmetic series, do the following: The first term is, is the number of terms to discover, and is the common difference between the first and last terms in the series Figure out which of the following arithmetic sequence’s 18th term is correct.

- Then, using the formula that was provided before the question, write: To find any term in an arithmetic series, use the following formula:where is the first term, is the number of terms to be found, and is the common difference between the terms in the sequence.
- Then, using the remainder of the equation provided before the question, complete the sentence.
- 1, 5, 9, 13,.
- Explanation: The eleventh term signifies that there are a total of ten intervals between the first term and the eleventh term.

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.

## SOLUTION: Hello, my name is kevin i need help with this 2 questions; Write an equation from the nth term of the architmetic sequence. Then find a10. 15. -2,5,12,19. 16. 13,9,5,1. P

Question 1009259:Hello, my name is kevini need help with this 2 questions;Write an equation from the nth term of the architmetic sequence. Then find a10.15. -2,5,12,19.16. 13,9,5,1.Please say answer to both problems and all work thanks(Scroll Down for Answer!) | Did you know thatAlgebra.Comhas hundreds of free volunteer tutors who help people with math homework? Anyone can ask a math question, and most questions get answers!OR get immediatePAIDhelp on: |

## 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. Calculate the general term for the following numbers: a1=5
- D=3
- A1=12
- D=2
- A1=15
- D=5
- A1=7
- D=4
- D=1
- A1=23
- D=13
- A 1=1
- D=12
- A1=54
- D=14
- A1=1.8
- D=0.6
- A1=4.3
- D=2.1

- Find a formula for the general term based on the arithmetic sequence and apply it to get the 100 th term based on the series. 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.

- Calculate a formula for the general term based on the terms of an arithmetic sequence: a1=6anda7=42
- A1=12anda12=6
- A1=19anda26=56
- A1=9anda31=141
- A1=16anda10=376
- A1=54anda11=654
- A3=6anda26=40
- A3=16andananda15=

- Find all possible arithmetic means between the given terms: a1=3anda6=17
- A1=5anda5=7
- A2=4anda8=7
- A5=12anda9=72
- A5=15anda7=21
- A6=4anda11=1
- A7=4anda11=1

### Part B: Arithmetic Series

- Make a calculation for the provided total based on the formula for the general term 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

- Consider the following values: n=1160(3n)
- N=1121(2n)
- N=1250(4n3)
- N=1120(2n+12)
- N=170(198n)
- N=1220(5n)
- N=160(5212n)
- N=151(38n+14)
- N=1120(1.5n2.6)
- N=1175(0.2n1.6)
- 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 integers
- The sum of the first 200 positive odd integers
- The sum of the first 50 positive even integers
- The sum of the first 200 positive even integers
- The sum of the first 100 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

- Is the Fibonacci sequence an arithmetic series, or is it a mathematical 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 certain situations? Make a personal example to illustrate your point
- Discuss strategies for computing sums in situations when the index does not begin at one (1). n=1535(3n+4)=1,659 is an example of the number n=1535(3n+4)=1,659 Carl Friedrich Gauss was once accused of misbehaving at school, according to a well-known legend. As a punishment, his instructor assigned him the chore of adding the first 100 integers to his list of disciplinary measures. Apparently, Gauss responded accurately within seconds, according to mythology. In what way do you believe he was able to come up with the solution so rapidly, and how do you think he did it?

- 2,450, 90, 7,800, 4,230, 38,640, 124,750, 18,550, 765, 10,000, 20,100, 2,500, 2,550, K2, 294 seats, 247 bricks, $794,000, and

## Let a1,a2,.a10 be an arithmetic sequence. If a1+a3+a5+a7+a9=17 and a2+a4+a6+a8+a10=15

- Determining the mathematical or geometric nature of each series is your task. Find the following three terms on the list. fourteen, nineteen, twenty-four, thirty. A.geometric, 34, 39, and 44 B.arithmetic, 32, 36, and 41 C.arithmetic, 34, 39, and 44 D.arithmetic, 34, 39, and 44 In fact, the sequence is neither geometric nor symmetrical.

### math

- Determining the mathematical or geometric nature of each series is your task. Find the following three terms on the list. 1. the numbers 14, 19, 24, 29,. (1 point) geometric, 34, 39, 44 arithmetic, 32, 36, 41 arithmetic, 34, 39, 44 geometric, 34, 39, 44 arithmetic, 34, 39, 44 *** The sequence is neither geometric nor arithmetic.

### Algebra

- How do you know what the next two words in the following sequence are? 1, 5, and 9 are the digits of the number one. The following are the numbers: A. 27, 211 B. 10,11 C.12,15 and D.13,17 2 arithmetic sequences are instances of which of the following are true? Select all of the options that apply. A. -2,2,6,10 B. 1,3,9,27 C. 5,10,20,40 A. -2,2,6,10 B. 1,3,9,27 C. 5,10,20,40

### Mathematics: Arithmetic Sequence

- When arithmetic sequences are repeated, the fifth term and the eighth term are 18 and 27, respectively. 1. Locate the first term of the arithmetic series as well as the common difference between them. In this step, you will find the general term of the arithmetic sequence.

## Solve 100,110,120,130 Tiger Algebra Solver

The numbers 100, 110, 120, and 130 in your input appear to represent an arithmetic sequence.

#### Find the difference between the members

- An a 2 + an a 1 =110-100= 10
- A 3 + an a 2 =120-110= 10
- And an a 3 + an a 3 =130-120= 10

Throughout the series, there is a constant difference between every two adjacent members, which is equal to 10.

#### General Form: a n =a 1 +(n-1)d

A 1 equals one hundred (this is the 1st member) a n =130 (this is the member who is the last/n th) d=10 is the decimal equivalent of ten (this is the difference between consecutive members) n=4 is the number of participants (this is the number of members)

#### Sum of finite series members

An arithmetic series is a collection of components of a finite arithmetic progression that are added together. Consider the following total, which is based on our example: 100+110+120+130 If you know the number of words being added (in this case 4), multiply it by the sum of the first and final numbers in the progression (in this case 100 + 130 = 230), then divide the result by two: 4(100+130) = 230.

2 The total of the four components of this series equals 460 dollars. In the following straight liney=10x+100, this series corresponds to the number 10.

#### Finding the n thelement

- A 1 equals a 1 plus (n-1) *d is more than 100. (1-1) *10 equals 100
- A 2 equals a 1 plus (n-1) *d is more than 100. (2-1) *10 equals 110
- A 3 equals a 1 plus (n-1) *d is more than 100. (3-1) *10 equals 120
- A 4 equals a 1 plus (n-1) *d is more than 100. (4-1) *10 equals 130
- A 5 equals a 1 plus (n-1) *d is more than 100. (5-1) *10 equals 140
- A 6 equals a 1 plus (n-1) *d is more than 100. (6-1) *10 equals 150
- A 7 equals a 1 plus (n-1) *d is more than 100. (7-1) *10 =160
- An 8 equals a 1 plus (n-1) *d is more than 100. (8-1) *10 equals 170
- A 9 equals a 1 plus (n-1) *d is more than 100. (9-1) *10 =180
- A 10=a 1 +(n-1)*d =100+
- A 10=a 1 +(n-1)*d =100+ (10-1) *10 =190
- An 11=a 1 +(n-1)*d =100+
- An 11=a 1 +(n-1)*d =100+ (11-1) *10 equals 200
- A 12 equals a 1 plus (n-1) *d is more than 100. (12-1) *10 equals 210
- A 13 equals a 1 plus (n-1) *d is more than 100. (13-1) *10 equals 220
- A 14 equals a 1 plus (n-1) *d is more than 100. (14-1) *10 =230
- A 15=a 1 +(n-1)*d =100+
- A 15=a 1 +(n-1)*d =100+ (15-1) *10 =240
- A 16 equals a 1 plus (n-1) *d is more than 100. (16-1) *10 equals 250
- A 17 equals a 1 plus (n-1) *d is more than 100. (17-1) *10 equals 260
- An 18 equals a 1 plus (n-1) *d is more than 100. (18-1) *10 =270
- A 19=a 1 +
- A 10 =270 (n-1) *d is more than 100. (19-1) *10 equals 280
- A 20 equals a 1 plus (n-1) *d is more than 100. (20-1) *10 equals 290
- A 21 equals a 1 plus (n-1) *d is more than 100. (21-1) *10 equals 300
- A 22 equals a 1 plus (n-1) *d is more than 100. (22-1) *10 equals 310
- A 23 equals a 1 plus (n-1) *d is more than 100. (23-1) *10 equals 320
- A 24 equals a 1 plus (n-1) *d is more than 100. (24-1) *10 =330
- A 25=a 1 +(n-1)*d =100+
- A 25=a 1 +(n-1)*d =100+ (25-1) *10 =340
- A 26=a 1 +(n-1)*d =100+
- A 26=a 1 +(n-1)*d =100+ (26-1) The number 10 equals 350
- The number 27 equals one plus one (n-1) *d is more than 100. (27-1) *10 =360
- A 28 equals a 1 plus (n-1) *d is more than 100. (28-1) *10 =370
- A 29 equals a 1 plus (n-1) *d is more than 100. (29-1) 380 divided by ten

## Arithmetic sequences calculator that shows work

This online tool can assist you in determining the first $n$ term of an arithmetic progression as well as the total of the first $n$ terms of the progression. This calculator may also be used to answer even more complex issues than the ones listed above. For example, if $a 5 = 19 $ and $S 7 = 105$, the calculator may calculate the common difference ($d$) between the two numbers. Probably the most significant advantage of this calculator is that it will create all of the work with a thorough explanation.

+ 98 + 99 + 100 =?

In an arithmetic series, the first term is equal to $frac$, and the common difference is equal to 2.

An arithmetic series has a common difference of $7$ and its eighth term is equal to $43$, with the common difference being $7$.

Suppose $a 3 = 12$ and the sum of the first six terms is equal to 42.

When the initial term of an arithmetic progression is $-12$, and the common difference is $3$, then the progression is complete.

## About this calculator

An arithmetic sequence is a list of integers in which each number is equal to the preceding number plus a constant, as defined by the definition above. The common difference ($d$) is a constant that is used to compare two things. Formulas:The $n$ term of an arithmetic progression may be found using the $color$ formula, where $color$ is the first term and $color$ is the common difference between the first and second terms. These are the formulae for calculating the sum of the first $n$ numbers: $colorleft(2a 1 + (n-1)d right)$ and $colorleft(a 1 + a right)$, respectively.