Question

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

−15, −12, −9, −6, −3, …

Short answer

The obtained value is 855.

Step-by-step solution

Step 1. Given Information. 

The arithmetic sequence is −15, −12, −9, −6, −3, ….

Step 2. Find the common difference d. 

Find the common difference of consecutive terms.

$\begin{array}{rcl}d& =& -12-\left(-15\right)\\ & =& 3\end{array}$

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

$\begin{array}{rcl}{a}_{30}& =& -15+\left(30-1\right)3\\ & =& -15+87\\ & =& 72\end{array}$

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.

$\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(-15+72\right)\\ & =& 15\left(57\right)\\ & =& 855\end{array}$