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)