The sum to $n$ terms of an AP is $3 n^2+5 n$. If its $m^{ ext {th }}$ term is 164 , then $\mathrm{m

Question

The sum to $n$ terms of an AP is $3 n^2+5 n$. If its $m^{	ext {th }}$ term is 164 , then $\mathrm{m}=$

Professor PC Thomas Classes · Answer

$ \begin{array}{r} \mathrm{t}_{\mathrm{m}}=\mathrm{S}_{\mathrm{m}}-\mathrm{S}_{\mathrm{m}-1}=3\left|\mathrm{~m}^2-(\mathrm{m}-1)^2ight|+5[\mathrm{~m}-(\mathrm{m}-1)] 4 \ =16 \end{array} $