Q6 of 176 Page 8

If the nth term of an A.P. is (2n + 1), find the sum of first n terms of the A.P.

Given: an = 2n + 1


Taking n = 1,


a1 = 2(1) + 1 = 2 + 1 = 3


Taking n = 2,


a2 = 2(2) + 1 = 4 + 1 = 5


Taking n = 3,


a3 = 2(3) + 1 = 6 + 1 = 7


Therefore the series is 3, 5, 7, …


So, a = 3, d = a2 – a1 = 5 – 3 = 2


Now, we have to find the sum of first n terms of the AP






⇒ Sn = 2n + n2


Hence, the sum of n terms is n2 + 2n.


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