Question

What is the sum of first n terms of the AP a, 3a, 5a, ....

Answer 1

The given AP is 3a,5a,........
Here,
First term, A = a
Common difference, D = 3a - a = 2a
 ∴ Sum of the n terms, n S

`= n/2 [2xx a+ (n-1) xx 2a]          { s_n = n/2 [ 2A +(n-1) D]}`

`= n/2 (2a + 2an -2a )`

`= n/2 xx 2 an`

= an²

Hence, the required sum is an² .