If the sum of n terms of an AP is (3n2 + 5n) and its mth term is 164, find the value of m.

To Find: m


Given: Sum of n terms, mth term


Put n = 1 to get the first term


So a1 = 3 + 5 = 8


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


So a1 + a2 = 12 + 10 = 22


So a2 = 14


Common difference = 14 - 8 = 6


Tn = a + (n - 1)d = 8 + (n - 1)6 = 6n + 2


Now 6m + 2 = 164


Or m = 27


The value of m is 27.


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