If the sum of $n$ terms of an $A . P$ is $3 n^{2} + 5 n$ and its $m^{t h}$ term is 164, then value of $' m'$ is

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$26$

$22$

$25$

$27$

answer is C.

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Detailed Solution

$\begin{array}{l} a_{m} = S_{m} - S_{m - 1} \\ 164 = 3 m^{2} + 5 m - 3 {(m - 1)}^{2} - 5 (m - 1) \\ = 3 m^{2} + 5 m - 3 m^{2} + 6 m - 3 - 5 m + 5 \\ 164 = 6 m + 2 \\ 6 m = 162 \\ m = \frac{162}{6} = 27 \end{array}$

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