Question

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

Answer 1

Sum of first n terms = S_n = (3n² + 5n)

Sum of one term = S₁ = 3(1)² + 5(1) = 8 = first term

Sum of first two terms = S₂ = 3(2)² + 5(2) = 22

We know that, second term = a₂ = S₂ – S₁

=22 – 8

= 14

=> a₂ = 14

Now, d = a₂ – a₁

= 14 – 8 = 6

Answer: Common difference is 6.