If sum of $n$ terms of an A.P. is $3 n^{2} + 5 n$ and $T_{m} = 164,$ then $m =$

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Solution

The correct option is B 27
We know that, $T_{m} = S_{m} - S_{m - 1}$
$S_{m} = 3 m^{2} + 5 m$
$s_{m - 1} = 3 (m - 1)^{2} + 5 (m - 1)$
$= 3 (m^{2} + 1 - 2 m) + 5 m - 5$
$= 3 m^{2} + 3 - 6 m + 5 m - 5$
$= 3 m^{2} - m - 2$
$\Rightarrow S_{m} - S_{m - 1} = 3 m^{2} + 5 m - 3 m^{2} + m + 2$
$\Rightarrow 6 m + 2 = 164$
$\Rightarrow 6 m = 162$
$\Rightarrow m = 27$

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