Q. 63.7( 3 Votes )

# The sum of first n terms of an AP is (3n^{2} + 6n). The common difference of the AP is

A. 6

B. 9

C. 15

D. - 3

Answer :

Let S_{n} denotes the sum of first n terms of an AP.

Sum of first n terms = S_{n} = 3n^{2} + 6n

Then n^{th} term is given by: a_{n} = S_{n} - S_{n - 1}

∴ a_{n} = (3n^{2} + 6n) - [3(n - 1)^{2} + 6(n - 1)]

= (3n^{2} + 6n) - [3(n^{2} + 1 - 2n) + 6n - 6]

= 3n^{2} + 6n - 3n^{2} - 3 + 6n - 6n + 6

= 3 + 6n

Now, common difference = d = a_{n} - a_{n - 1}

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

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

= 6

∴ Common difference = 6

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