Q. 63.7( 3 Votes )

The sum of first n terms of an AP is (3n2 + 6n). The common difference of the AP is
A. 6

B. 9

C. 15

D. - 3

Answer :

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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