What Is The Sum Of The Arithmetic Sequence 3, 9, 15 , If There Are 34 Terms? (Perfect answer)

The sum of the arithmetic sequence 3, 9, 15, if there are 34 terms is 3468.

Contents

What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms 5 points?

Summary: The sum of the arithmetic sequence 3, 9, 15, if there are 26 terms is 2028.

What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?

The sum of the arithmetic sequence 3, 9, 15, if there are 24 terms is 1728.

What is the sum of the arithmetic sequence 3 9 15 if there are 22 terms 5 points?

The sum of the arithmetic sequence 3, 9, 15, if there are 22 terms is 1452.

What is the sum of the arithmetic sequence 3 9 15 if there are 36 terms?

The sum of the arithmetic sequence 3, 9, 15, if there are 36 terms is 3888.

What is the sum of geometric sequence 1/3 9?

What is the sum of the geometric sequence 1, 3, 9, if there are 10 terms? Therefore, the sum of the geometric sequence is 29524.

What is the sum of the geometric sequence 1 3 9 if there are 11 terms?

Summary: The sum of the geometric sequence 1, 3, 9, if there are 11 terms is 88573.

What is the sum of the geometric sequence 1 3 9 if there are 14 terms?

Summary: The sum of the geometric sequence 1, 3, 9, if there are 14 terms is 2391484.

What is the sum of the geometric sequence 1 3 9 if there are 12 terms?

Summary: The sum of the geometric sequence 1, 3, 9, if there are 12 terms is 265720.

What is the next term in the arithmetic sequence 3 9 15?

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 finite sequence?

A sequence is finite if it has a limited number of terms and infinite if it does not. Finite sequence: {4,8,12,16,…, 64} The first of the sequence is 4 and the last term is 64. Since the sequence has a last term, it is a finite sequence.

What is the term in finding the sum of the nth term a geometric sequence?

For r≠1 r ≠ 1, the sum of the first n terms of a geometric series is given by the formula s=a1−rn1−r s = a 1 − r n 1 − r.

What is the sum of the arithmetic sequence 3, 9, 15…, if there are 22 terms?

Assuming that there are n initial terms in the sequence and that the difference between the first term and the difference between terms is d, the total of all of the first n terms is provided bya + (a+d) +, and the sum of all of the second terms is given bya+2d, and so on (n-1) d = sum (k=0) is a mathematical expression. (n-1)(a+kd) = n((a 1+a n)/2)where a i is the ith term in the series (so a 1 = a and a n = a + (n-1)d) and n is the number of terms in the sequence. (The derivation of this formula is provided further below.) Applying the method here with a = 3 and d = 6 results in the following: The sum of three nines and fifteens is plus.

In the following, we will show how to derive the arithmetic sum formula, which is not necessarily essential in order to solve the previously stated issue.

What Is The Sum Of The Arithmetic Sequence 3, 9, 15., If There Are 34 Terms?

If there are 36 terms in the arithmetic sequence 3 9 15, what is the sum of the series? The total of all of this is 3888. Furthermore, if there are 24 terms in the arithmetic series 3 9 15, what is the sum of the sequence? The following is the formula for the sum of an arithmetic sequence: Substitute: The answer is 1728. Finally, if there are 22 terms in the arithmetic series 3 9 15, what is the sum of the sequence? As a result, the first option, 1452, is the correct answer.

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Frequently Asked Question:

To achieve this, add the two integers together and divide the result by two. Multiply the average by the number of terms in the series to get the final result. The sum of the arithmetic sequence will be returned as a result of this. As a result, the total of the numbers 10, 15, 20, 25, and 30 equals 100.

How do you find the sum of an arithmetic sequence?

It is possible to calculate the total of anarithmetic series by multiplying the number of terms by the average of the first and final terms. For example, the sum of 3 + 7 + 11 + 15 + 99 has a 1 = 3 and a d = 4. Make use of the explicit formula for anarithmetic sequence to locate n.

What is the sum of the terms in a sequence?

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

How can you find the sum of the terms of the arithmetic sequence if the number of terms 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 arithmetic sequence 3 9 15 if there are 24 terms?

The following is the formula for the sum of an arithmetic sequence: Answer: 1,728. Substitute: 1,728.

What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms 5 points?

The sum of anarithmetic series is: S = n*(a 1+a n)/2, which is straightforward. In your example, n is the number of words, which is 26. The value of a n is a 26.

How do you find the sum of the terms in an arithmetic sequence?

To achieve this, add the two integers together and divide the result by two. Multiply the average by the number of terms in the series to get the final result. The sum of the arithmetic sequence will be returned as a result of this. As a result, the total of the numbers 10, 15, 20, 25, and 30 equals 100.

What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms 5 points?

The sum of anarithmetic series is: S = n*(a 1+a n)/2, which is straightforward. In your example, n is the number of words, which is 26. The value of a n is a 26.

How do you find the sum of the terms in an arithmetic sequence?

To achieve this, add the two integers together and divide the result by two. Multiply the average by the number of terms in the series to get the final result. The sum of the arithmetic sequence will be returned as a result of this. As a result, the total of the numbers 10, 15, 20, 25, and 30 equals 100.

What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?

The following is the formula for the sum of an arithmetic sequence: Answer: 1,728. Substitute: 1,728.

What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms 5 points?

The sum of anarithmetic series is: S = n*(a 1+a n)/2, which is straightforward. In your example, n is the number of words, which is 26. The value of a n is a 26.

What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?

The following is the formula for the sum of an arithmetic sequence: Substitute: The answer is 1728. (It has been visited 1 time, with 1 visit today)

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.

Take a moment to confirm that this equation accurately reflects the sequence you’ve been given. 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.

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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

  1. 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
  2. 12 and 2
  3. 15 and 5
  4. 7 and 4 respectively
  5. 12 and 1
  6. A1=23 and 13 respectively
  7. 1 and 12 respectively
  8. A1=54 and 14. The values of a1 are 1.8 and 0.6
  9. 4.3 and 2.1
  10. And a1=5.4 and 2.1 respectively.
  1. 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,.
  2. 4.4, 7.5, 13.7, 16.8,.
  3. 3, 8, 13, 18, 23,.
  4. 3, 7, 11, 15, 19,.
  5. 6, 14, 22, 30, 38,.
  6. 5, 10, 15, 20, 25,.
  7. 2, 4, 6, 8, 10,.
  8. 12,52,92,132,.
  9. 13, 23, 53,83,.
  10. 14,12,54,2,114,. Find the positive odd integer that is 50th
  11. Find the positive even integer that is 50th
  12. Find the 40 th term in the sequence that consists of every other positive odd integer in the following format: 1, 5, 9, 13,.
  13. Find the 40th term in the sequence that consists of every other positive even integer: 1, 5, 9, 13,.
  14. Find the 40th term in the sequence that consists of every other positive even integer: 2, 6, 10, 14,.
  15. 2, 6, 10, 14,. What number is the term 355 in the arithmetic sequence 15, 5, 5, 15, 25,.
  16. What number is the phrase 172 in the arithmetic sequence 4, 4, 12, 20, 28,.
  17. What number is the term 355 in the arithmetic sequence 15, 5, 5, 15, 25,.
  18. 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
  19. 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
  20. This is the problem.
  1. 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
  2. 1 = 12 and 12= 6
  3. 1 = 19 and 26 = 56
  4. 1 = 9 and 31 = 141
  5. 1 = 16 and 10 = 376
  6. 1 = 54 and 11 = 654. 1 = 6 and 7 = 42
  7. 1= 9 and 31 = 141
  8. 1 = 6 and 7
  1. Find all of the arithmetic means that exist between the two supplied terms. a1=3anda6=17
  2. A1=5anda5=7
  3. A2=4anda8=7
  4. A5=12anda9=72
  5. A5=15anda7=21
  6. A6=4anda11=1
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Part B: Arithmetic Series

  1. In light of the general term’s formula, figure out how much the suggested total is. an=3n+5
  2. S100
  3. An=5n11
  4. An=12n
  5. S70
  6. An=132n
  7. S120
  8. An=12n34
  9. S20
  10. An=n35
  11. S150
  12. An=455n
  13. S65
  14. An=2n48
  15. S95
  16. An=4.41.6n
  17. S75
  18. An=6.5n3.3
  19. S67
  20. An=3n+5
  1. Evaluate. 1160(3n)
  2. 1121(2n)
  3. 1250(4n-3)
  4. 1120(2n+12)
  5. 170 (198n)
  6. 1220(5n)
  7. 160(5212n)
  8. 151(38+14
  9. 1120(1.5n+2.6)
  10. 1175(0.2N1.6)
  11. 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.
  1. 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
  2. The sum of the first 200 positive odd integers
  3. The sum of the first 500 positive odd integers
  4. The sum of the first 50 positive even numbers
  5. The sum of the first 200 positive even integers
  6. The sum of the first 500 positive even integers
  7. The sum of the firstk positive odd integers
  8. The sum of the firstk positive odd integers the sum of the firstk positive even integers
  9. The sum of the firstk positive odd integers
  10. 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
  11. 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

  1. 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
  2. Discuss strategies for computing sums in situations when the index does not begin with one. For example, n=1535(3n+4)=1,659
  3. N=1535(3n+4)=1,659
  4. 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

  1. An=3n+2
  2. An=5n+3
  3. An=6n
  4. An=3n+2
  5. An=6n+3
  6. An=6n+2
  1. 1,565,450, 2,500,450, k2,
  2. 90,800, k4,230,
  3. 38640, 124,750,
  4. 18,550, k765
  5. 10,578
  6. 20,100,
  7. 2,500,550, k2,
  8. 294 seats, 247 bricks, $794,000, and so on.

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