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Q 108.

Expert-verifiedFound in: Page 1185

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.

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

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.

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

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

$\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(12+186\right)\\ & =& 15\left(198\right)\\ & =& 2970\end{array}$

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