Question

If the sum of $n$ terms of an A.P. is $3n^2+5n$ and its $m^{th}$term is $164,$ find the value of $m$.

Answer 1

Given, $s_n=3n^2+5n,a_m=164$
We know,
$a_n=s_n-s_{n-1}$
$=3n^2+5n-3(n-1{)}^2-5(n-1)$
$=3n^2+5n-3n^2+6n-3-5n+5$
$\therefore a_n=6n+2$
$\Rightarrow a_m=6m+2$
$\Rightarrow 164=6m+2$
$\Rightarrow 6m=162$
$\Rightarrow m=27$

Final answer : Hence, the value of $m=27$