# 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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