If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?

Here, Sn = 3n2 + 5n


S1 = a1 = 3 + 5 = 8


S2 = a1 + a2 = 12 + 10 = 22


⇒ a2 = S2 – S1 = 22 – 8 = 14


S3 = a1 + a2 + a3 = 27 + 15 = 42


⇒a3 = S3 – S2 = 42 – 22 = 20


∴ Given AP is 8, 14, 20, .....


Thus a = 8, d = 6


Given tm = 164.


164 = [a + (n –1)d]


164 = [(8) + (m –1)6]


164 = [8 + 6m – 6]


164 = [2 + 6m]


162 = 6m


m = 162 / 6.


∴ m = 27.

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