If the sum of n terms of an A.P. be 3$\mathbf{n}^{2}$ + n and its common difference is 6, then its first term is.
A. 2 B. 3 C. 1 D. 4 Answer: Option DShow Answer
Solution(By Apex Team)
Sum of n terms of an A.P. = 3$n^{2}$ + n
and common difference (d) = 6
Let first term be a, then
$\begin{aligned}&\therefore S_n=\frac{n}{2}[2a+(n-1)d]=3n^2+n\\
&\Rightarrow\frac{n}{2}[2a+(n-1)6]=3n^2+n\\
&\Rightarrow2a+6n-6=\left(3n^2+n\right)\times\frac{2}{n}\\
&\Rightarrow2a+6n-6=n\frac{(3n+1)\times2}{n}\\
&\Rightarrow2a+6n-6=(3n+1)2\\
&\Rightarrow2a+6n-6=6n+2\\
&\Rightarrow2a=6n+2-6n+6\\
&\Rightarrow2a=8\\
&\therefore a=\frac{8}{2}\\
&=4\end{aligned}$
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