Question

Find $S_{15}$ if the A.P. is $2,5,8,....?$

Answer 1

Given A.P is $2,5,8,...$

The first term, $a=2$.

The common difference, $d=5-2$

$=3$

The sum of first n terms of an A.P is given by

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$\therefore S_{15}=\frac{15}{2}[2\times 2+(15-1)\times 3]$

$=\frac{15}{2}[4+14\times 3]$

$=15\times 2+15\times 3\times 7$

$=345$