Question

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

$11,14,17,20,23,\dots$

Short answer

The obtained sum is 1635.

Step-by-step solution

Step 1. Given Information.

The arithmetic sequence is$11,14,17,20,23,\dots$.

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl}d& =& 14-11\\ & =& 3\end{array}$

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

$\begin{array}{rcl}{a}_{30}& =& 11+\left(30-1\right)3\\ & =& 11+87\\ & =& 98\end{array}$

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 thirteenth term.

$\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(11+98\right)\\ & =& 15\left(109\right)\\ & =& 1635\end{array}$