If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6,
Question:

If the sum of $n$ terms of an A.P. be $3 n^{2}+n$ and its common difference is 6 , then its first term is

(a) 2

(b) 3

(c) 1

(d) 4

Solution:

In the given problem, the sum of n terms of an A.P. is given by the expression,

$S_{n}=3 n^{2}+n$

Here, we can find the first term by substitutingas sum of first term of the A.P. will be the same as the first term. So we get,

$S_{n}=3 n^{2}+n$

$S_{1}=3(1)^{2}+(1)$

$=3+1$

$=4$

Therefore, the first term of this A.P is $a=4$. So, the correct option is (d).