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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q 12.36. (page 1181)

Find the sum of the first 30 terms of the arithmetic sequence: 7, 10, 13, 16, 19, ….

Short Answer

Expert verified

The obtained sum is 1515.

Step by step solution

01

Step 1. Given Information.

Consider the given sequence:

$7, 10, 13, 16, 19, \dots$

02

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl} d & = & 10 - 7 \\ = & 3 \end{array}$

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

$\begin{array}{rcl} a_{30} & = & 7 + (30 - 1) 3 \\ = & 7 + 87 \\ = & 94 \end{array}$

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.

$\begin{array}{rcl} S_{30} & = & \frac{30}{2} (7 + 94) \\ = & 15 (101) \\ = & 1515 \end{array}$

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Most popular questions from this chapter

Expand the partial sum and find its value: $\sum_{i = 1}^{5} 3 i$

Write the sum using summation notation: $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} .$

In the following exercises, expand each binomial using Pascal's Triangle.

$(3 x - 4)^{4}$

In the following exercises, expand each binomial using Pascal's Triangle.

$(x + 4)^{4}$

In the following exercises, expand each binomial using Pascal's Triangle.

$(m + n)^{10}$

See all solutions

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