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.