# If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.

Given. Sn = 3n2 + 5n

S1 = 3(1)2 + 5 × 1 = 8 ⇒ T1 = 8
S2 = 3(2)2 + 5 × 2 = 22

Thus T1 + T2 = 22

or 8 + T2 = 22

or T2 = 14

Now a = 8, d = 14 – 8 = 6

As Tm = 164
or a +(m – 1)d = 164
or 8 + (m – 1) (6) = 164
or 8 + 6m – 6 = 164
or 6m = 162
or m = = 27
Hence m = 27

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