# The sum of first n terms of an AP is (3n2 + 6n). The common difference of the AP isA. 6B. 9C. 15D. - 3

Let Sn denotes the sum of first n terms of an AP.

Sum of first n terms = Sn = 3n2 + 6n

Then nth term is given by: an = Sn - Sn - 1

an = (3n2 + 6n) - [3(n - 1)2 + 6(n - 1)]

= (3n2 + 6n) - [3(n2 + 1 - 2n) + 6n - 6]

= 3n2 + 6n - 3n2 - 3 + 6n - 6n + 6

= 3 + 6n

Now, common difference = d = an - an - 1

= 3 + 6n - [3 + 6(n - 1)]

= 3 + 6n - 3 - 6n + 6

= 6

Common difference = 6

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