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

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Solution

$T_{m}$ = $S_{m}$ - $S_{m - 1}$

$∴$ 164 = 3 $m^{2}$ +5m - (3 $(m - 1)^{2}$ +5(m-1))

164 = 3 (2m-1) + 5.1

$\Rightarrow$ 6m = 162

$\Rightarrow$ m = 27.

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

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