Question

The sum of the first $n$ terms of an A.P is $3n^2+6n$. Find the $n$th term of this A.P.

• A. $5n+3$
• B. $6n+3$
• C. $6n+5$
• D. None of these

Answer 1

The correct option is B $6n+3$

Formula,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Given,

$S_n=3n^2+6n$

equating both the terms, we get,

$2a+(n-1)d=18+6(n-1)$

comparing LHS and RHS, we get,

$2a=18\Rightarrow a=9$

$d=6$

nth term is given by,

$T_n=a+(n-1)d$

$=9+(n-1)6$

$=9+6n-6$

$\therefore T_n=6n+3$