Question

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

8, 5, 2, −1, −4, …

Short answer

The obtained sum is -1065.

Step-by-step solution

Step 1. Given Information.

The arithmetic sequence is $8,5,2,-1,-4,\dots$.

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl}d& =& 5-8\\ & =& -3\end{array}$

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

$\begin{array}{rcl}{a}_{30}& =& 8+\left(30-1\right)\left(-3\right)\\ & =& 8-87\\ & =& -79\end{array}$

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="1645453590666" $\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(8-79\right)\\ & =& 15\left(-71\right)\\ & =& -1065\end{array}$