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

1.	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
Answer» (D) 4 Explanation: To find: Common Difference of A.P that is d Consider, S_n = 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)

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

Answer»

(D) 4

Explanation:

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

Consider,

S_n = 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)