# Sum of $n$ terms of AP is $6n^2+5n$ while $a_{m}=164$, the value of $m$ is

$(a)\;\frac{55}{4}\qquad(b)\;\frac{56}{4}\qquad(c)\;15\qquad(d)\;\frac{59}{4}$

Answer : (a) $\;\frac{55}{4}$
Explanation : $a_{m}=S_{m}-S_{m-1}$
$=6m^2+5m-6\;(m-1)^2-5(m-1)$
$=12m-1$
$164=12m-1$
$m=\frac{55}{4}.$
answered Jan 21, 2014 by