Question

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.

−17, −15, −13, −11, −9, …

Short answer

The obtained sum is 360.

Step-by-step solution

Step 1. Given Information.

The arithmetic sequence is −17, −15, −13, −11, −9, ….

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl}d& =& -15-\left(-17\right)\\ & =& 2\end{array}$

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

$\begin{array}{rcl}{a}_{30}& =& -17+\left(30-1\right)2\\ & =& -17+58\\ & =& 41\end{array}$

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.

localid="1645454460792" $\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(-17+41\right)\\ & =& 15\left(24\right)\\ & =& 360\end{array}$