Very-Short and Short-Answer Questions

The given AP is a, 3a, 5a, ... .  

Here,

First term, A = a

Common difference, D = 3a − a = 2a

∴ Sum of first n terms, Sn

$=\frac{n}{2}[2 \times a+(n-1) \times 2 a] \quad\left\{S_{n}=\frac{n}{2}[2 A+(n-1) D]\right\}$

$=\frac{n}{2}(2 a+2 a n-2 a)$

$=\frac{n}{2} \times 2 a n$

$=a n^{2}$

Hence, the required sum is an2.