Question

Find the sum of the first 30 terms of the arithmetic sequence: 7, 10, 13, 16, 19, ….

Short answer

The obtained sum is 1515.

Step-by-step solution

Step 1. Given Information.

Consider the given sequence:

$7,10,13,16,19,\dots$

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl}d& =& 10-7\\ & =& 3\end{array}$

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

$\begin{array}{rcl}{a}_{30}& =& 7+\left(30-1\right)3\\ & =& 7+87\\ & =& 94\end{array}$

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.

$\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(7+94\right)\\ & =& 15\left(101\right)\\ & =& 1515\end{array}$