# If the sum of first n terms is (3n2 + 5n), find its common difference.

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

Sum of first n terms = Sn = 3n2 + 5n

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

an = (3n2 + 5n) - [3(n - 1)2 + 5(n - 1)]

= (3n2 + 5n) - [3(n2 + 1 - 2n) + 5n - 5]

= 3n2 + 5n - 3n2 - 3 + 6n - 5n + 5

= 2 + 6n

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

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

= 2 + 6n - 2 - 6n + 6

= 6

Common difference = 6

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

Sum of first n terms = Sn = 3n2 + 5n

Put n = 1, we get S1 = 8

Put n = 2, we get S2 = 22

Now S1 = a1

a2 = S2 - S1

a2 = 22 - 8 = 14

Now, d = a2 - a1

= 14 - 8

= 6

Common difference = 6

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