Question

Find each sum

$7+12+17+.....+(2+5n)$

Short answer

The solution is$S_n=\frac{n}{2}(9+5n)$

Step-by-step solution

Given information

$7+12+17+.....+(2+5n)$

Calculation

We have, $7+12+17+.....+(2+5n)$

So , $a_1=7,d=5,a_n=2+5n$

Now use formula,

$$\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ =\frac{n}{2}(7+2+5n) \\ =\frac{n}{2}(9+5n) \end{gathered}$$

The sum is$S_n=\frac{n}{2}(9+5n)$