Q. 3 B

The sum of n terms of an A.P. is 3n2+ 5n. Find the A.P. Hence, find its 16th term.

Answer :

Sn = 3n2 + 5n


Taking n = 1, we get


S1 = 3(1)2 + 5(1)


S1 = 3 + 5


S1 = 8


a1 = 8


Taking n = 2, we get


S2 = 3(2)2 + 5(2)


S2 = 12 + 10


S2 = 22


a2 = S2 – S1 = 22 – 8 = 14


Taking n = 3, we get


S3 = 3(3)2 + 5(3)


S3 = 27 + 15


S3 = 42


a3 = S3 – S2 = 42 – 22 = 20


So, a = 8,


d = a2 – a1 = 14 – 8 = 6


Now, we have to find the 15th term


an = a + (n – 1)d


a16 = 8 + (16 – 1)6


a16 = 8 + 15 × 6


a16 = 8 + 90


a16 = 98


Hence, the 16th term is 98.


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