Question

The sum of first $m$ terms of an A.P. is $4m^2-m$. If its $n^{th}$ term is $107$, find the value of $n$.

Answer 1

Sum of m terms, $S_m=4m^2-4m$

Let $a_n$ be $n^{th}$ term of A.P

$a_1=S_1=4(1{)}^2-1=3$

$S_n=\frac{n}{2}(a+a_n)$

$a_n=107$

$S_n=4n^2-n=\frac{n}{2}(a_1+a_n)$

$4n-1=\left(\frac{3+107}{2}\right)$

$4n-1=55$

$n=14$