Question

Find the sum of the first 30 terms of the arithmetic sequence: 5, 9, 13, 17, 21, ….

Short answer

The obtained sum is 1890.

Step-by-step solution

Step 1. Given Information.

The arithmetic sequence is$5,9,13,17,21,\dots$.

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl}d& =& 9-5\\ & =& 4\end{array}$

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

$\begin{array}{rcl}{a}_{30}& =& 5+\left(30-1\right)4\\ & =& 5+116\\ & =& 121\end{array}$

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.

$\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(5+121\right)\\ & =& 15\left(126\right)\\ & =& 1890\end{array}$