Q. 54.4( 8 Votes )

# If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?A. 26thB. 27thC. 28thD. none of these

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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