Question

The sum of the first n terms of an AP is (4n² + 2n). The nth term of this AP is

(a) (6n - 2) 

(b) (7n – 3) 

(c) (8n – 2) 

(d) (8n + 2)

Answer 1

Correct answer is (c) (8n - 2)

Let S_n denotes the sum of first n terms of the AP.

∴ S_n = 4n² + 2n

\(\Rightarrow\) S_n-1 = 4(n - 1)² + 2(n - 1)

= 4(n² - 2n + 1) + 2(n - 1)

∴ n^th term of the AP, an = S_n - S_n-1

= (4n² + 2n) - (4n² - 6n + 2)

= 8n - 2

Thus, the n^th term of thee AP is (8n - 2)