Question

If the sum of first n terms of an A.P. is \((4n^2 + 2n)\) then the common difference of A.P. is

(A) 6

(B) 14

(C) 8

(D) 4

Answer 1

Correct option is (C) 8

Let 'a' be the first term and 'd' be the common difference.

It is given that sum of the first n terms of an A.P. is \(4 n^2+2 n\).

\(\therefore\) First term (a) = \(S_1= 4(1)^2+2(1)=4+2=6\)

Sum of first two terms \(=S_2=4(2)^2+2(2)=16+4=20\)

\(\therefore\) Second term \(=S_2-S_1=20-6=14\)

\(\therefore\) Common difference (d) = Second term - First term

\(= 14 - 6\)

\(= 8\)