Question

Very-Short and Short-Answer Questions

What is the sum of first n terms of the AP a, 3a, 5a, ... . [CBSE 2012]

Answer 1

The given AP is a, 3a, 5a, ... .

Here,

First term, A = a

Common difference, D = 3a − a = 2a

∴ Sum of first n terms, S_n

$$\begin{gathered} =\frac{n}{2}\left[2\times a+\left(n-1\right)\times 2a\right]\left\{S_n=\frac{n}{2}\left[2A+\left(n-1\right)D\right]\right\} \\ =\frac{n}{2}\left(2a+2an-2a\right) \\ =\frac{n}{2}\times 2an \\ =a{n}^2 \end{gathered}$$

Hence, the required sum is an².