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

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Solution

The correct option is B
27

$T_{m} = S_{m} - S_{m - 1}$
$\Rightarrow 164 = 3 m^{2} + 5 m - 3 [3 (m - 1)^{2} + 5 ((m - 1)]$
$164 = 3 (2 m - 1) + 5 \times 1$
$6 m = 162 ⟹ m = 27$

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