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If the sum of n terms of an A.P.

Question:

 If the sum of n terms of an A.P. is given by Sn = 3n + 2n 2, then the common difference of the A.P. is

(A) 3

(B) 2

(C) 6

(D) 4

Solution:

(D) 4

Explanation:

To find: Common Difference of A.P that is d

Consider,

Sn = 3n + 2n2

Putting n = 1, we get

S1 = 3(1) + 2(1)2

= 3 + 2

S1 = 5

Putting n = 2, we get

S2 = 3(2) + 2(2)2

= 6 + 2(4)

= 6 + 8

S2 = 14

Now, we know that,

S1 = a1

⇒ a1 = 5

And a2 = S2 – S1

= 14 – 5

= 9

∴ Common Difference, d = a2 – a1

= 9 – 5

= 4

Hence, the correct option is (D)

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