Question

The sum of first n terms of an ap is 4n²+2n find the value of this ap

Answer 1

Given that sn = 4n^2 + 2n. --------------- (1)

Substitute n = 1 in (1), we get

sn = 4(1)^2 + 2(1)

= 4 + 2

= 6.


So, Sum of the first term of AP is 6 i.e a = 6.


Now,

Substitute n = 2 in (1), we get

sn = 4(2)^2 + 2(2)

= 4 * 4 + 2 * 2

= 16 + 4

= 20.

So, Sum of the first 2 terms = 20.


Now,

First-term + second term = 20

6 + a2 = 20

a2 = 20 - 6

a2 = 4.

Hence in AP,

first term a = 6.

common difference d = a2 - a1

= 14 - 6

= 8.


We know that sum of n terms of an AP an = a + (n - 1) * d

= 6 + (n - 1) * (8)

= 6 + 8n - 8

= 8n - 2.


Therefore the nth term of the AP = 8n - 2 (or) 2(4n - 1).