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 substituting
as 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).