Question

If the sum of first p terms of an AP is (ap² + bp), find its common difference.

Answer 1

Sum of first p terms = S_p = (ap² + bp)

Sum of one term = S₁ = a(1)² + b(1) = a+b = first term

Sum of first two terms = S₂ = a(2)² + b x 2 = 4a + 2b

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

= (4a + 2b) – (a + b)

= 3a + b

Now, d = a₂ – a₁

= 3a + b – (a+b)

= 2a

Answer: Common difference is 2a.