Question

The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its
A. 24th term

B. 27th term
C. 26th term
D. 25th term

Answer 1

Answer:

S = 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 = 6Given tm = 164.

164 = [a + (n –1)d]164 = [(8) + (m –1)6]164 = [8 + 6m – 6]164 = [2 + 6m]162= 6mm = 162 / 6.∴ m = 27.