Q. 3 A4.7( 9 Votes )

The sum of the first n terms of an A.P. is given by Sn = 2n2 + 5n , find the nth term of the A.P.

Answer :

Sn =2n2 + 5n


Taking n = 1, we get


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


S1 = 2 + 5


S1 = 7


a1 = 7


Taking n = 2, we get


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


S2 = 8 + 10


S2 = 18


a2 = S2 – S1 = 18 – 7 = 11


Taking n = 3, we get


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


S3 = 18 + 15


S3 = 33


a3 = S3 – S2 = 33 – 18 = 15


So, a = 7,


d = a2 – a1 = 11 – 7 = 4


Now, we have to find the 15th term


an = a + (n – 1)d


an = 7 + (n – 1)4


an = 7 + 4n – 4


an = 3 + 4n


Hence, the nth term is 4n + 3.


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