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Answers without the blur. Sign up and see all textbooks for free! Q 108.

Expert-verified Found in: Page 1185 ### Intermediate Algebra

Book edition OER 2017
Author(s) OPENSTAX
Pages 1346 pages
ISBN 9780998625720 # In the following exercises, find the sum of the first 30 terms of each arithmetic sequence. 12, 18, 24, 30, 36, …

The obtained sum is 2970.

See the step by step solution

## Step 1. Given Information.

The arithmetic sequence is $12,18,24,30,36,\dots$.

## Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl}d& =& 18-12\\ & =& 6\end{array}$

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

$\begin{array}{rcl}{a}_{30}& =& 12+\left(30-1\right)6\\ & =& 12+174\\ & =& 186\end{array}$

## Step 3. Use the sum formula.

Use the sum formula ${S}_{n}=\frac{n}{2}\left({a}_{1}+{a}_{n}\right)$ to find the sum of the thirtieth term.

$\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(12+186\right)\\ & =& 15\left(198\right)\\ & =& 2970\end{array}$ ### Want to see more solutions like these? 