Q2 of 176 Page 8

The sum of first n terms of an A.P. is given by Sn = 3n2 + 2n. Determine the A.P. and its 15th term.

Sn = 3n2 + 2n


Taking n = 1, we get


S1 = 3(1)2 + 2(1)


⇒ S1 = 3 + 2


⇒ S1 = 5


⇒ a1 = 5


Taking n = 2, we get


S2 = 3(2)2 + 2(2)


⇒ S2 = 12 + 4


⇒ S2 = 16


∴ a2 = S2 – S1 = 16 – 5 = 11


Taking n = 3, we get


S3 = 3(3)2 + 2(3)


⇒ S3 = 27 + 6


⇒ S3 = 33


∴ a3 = S3 – S2 = 33 – 16 = 17


So, a = 5,


d = a2 – a1 = 11 – 5 = 6


Now, we have to find the 15th term


an = a + (n – 1)d


a15 = 5 + (15 – 1)6


a15 = 5 + 14 × 6


a15 = 5 + 84


a15 = 89


Hence, the 15th term is 89 and AP is 5, 11, 17, 23,…


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