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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q 12.35. (page 1181)

Find the sum of the first 30 terms of the arithmetic sequence: 5, 9, 13, 17, 21, ….

Short Answer

Expert verified

The obtained sum is 1890.

Step by step solution

01

Step 1. Given Information.

The arithmetic sequence is $5, 9, 13, 17, 21, \dots$ .

02

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl} d & = & 9 - 5 \\ = & 4 \end{array}$

And, now find the 30th term of the sequence.

$\begin{array}{rcl} a_{30} & = & 5 + (30 - 1) 4 \\ = & 5 + 116 \\ = & 121 \end{array}$

03

Step 3. Use the sum formula.

Use the sum formula $S_{n} = \frac{n}{2} (a_{1} + a_{n})$ to find the sum of the thirteenth term.

$\begin{array}{rcl} S_{30} & = & \frac{30}{2} (5 + 121) \\ = & 15 (126) \\ = & 1890 \end{array}$

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Most popular questions from this chapter

Determine if each sequence is geometric. If so indicate the common ratio.

ⓐ. $7, 21, 63, 189, 567, 1, 701, \dots$

ⓑ. $64, 16, 4, 1, 1 4, 1 16, \dots$

ⓒ. $2, 4, 12, 48, 240, 1, 440, \dots$

Find the thirteenth term of a sequence where the first term is $81$ and the common ratio is $r = \frac{1}{3}$ .

In the following exercises, write the first five terms of each arithmetic sequence with the given first term and common difference.

$a_{1} = - 13$ and $d = 6$

Find the eleventh term of a sequence where the ninth term is 8 and the common difference is −3. Give the formula for the general term.

In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

$13, 9, 5, 1, - 3, - 7, . . . . .$

See all solutions

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