If the sum of n terms of an AP is


 If the sum of n terms of an AP is $\left(3 n^{2}+5 n\right)$ and its mth term is 164, find the value of m.




To Find: m

Given: Sum of $n$ terms, $m^{\text {th }}$ term

Put n = 1 to get the first term

So $a_{1}=3+5=8$

Put n = 2 to get the sum of first and second term

So $a_{1}+a_{2}=12+10=22$

So $a_{2}=14$

Common difference = 14 - 8 = 6

$T_{n}=a+(n-1) d=8+(n-1) 6=6 n+2$

Now 6m + 2 = 164

Or m = 27

The value of m is 27.

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