Question

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

12, 18, 24, 30, 36, …

Short answer

The obtained sum is 2970.

Step-by-step solution

Step 1. Given Information.

The arithmetic sequence is$12,18,24,30,36,\dots$.

Step 2. Find the common difference d.

Find the common difference of consecutive terms.

$\begin{array}{rcl}d& =& 18-12\\ & =& 6\end{array}$

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

$\begin{array}{rcl}{a}_{30}& =& 12+\left(30-1\right)6\\ & =& 12+174\\ & =& 186\end{array}$

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.

$\begin{array}{rcl}{S}_{30}& =& \frac{30}{2}\left(12+186\right)\\ & =& 15\left(198\right)\\ & =& 2970\end{array}$