Question

The sum of $n$ terms of an $A.P$ is $3n^2+n$. Then $8^{th}$ term of the $A.P$ is

• A. $46$
• B. $45$
• C. $47$
• D. $49$

Answer 1

The correct option is A $46$

Sum of $n$ terms of an $A.P.=\frac{n}{2}[2a+(n-1\left)d\right]$

$8^{th}$ term of an A.P. = $a+(n-1)d=a+7d$

$\frac{n}{2}[2a+(n-1\left)d\right]=3n^2+n\Rightarrow \frac{n}{2}[2a+(n-1\left)d\right]=n(3n+1)\Rightarrow 2a+(n-1)d=6n+2\Rightarrow 2a-d+nd=6n+2\Rightarrow 2a-d=2andd=6\Rightarrow a=4$

Hence. $8^{th}$ term=$a+7d=4+7\ast 6=4+42=46$