Let S_p denotes the sum of first p terms of an AP.

Sum of first p terms = S_p = ap² + bp

Then p^th term is given by: a_p = S_p - S_{p - 1}

∴ a_p = (ap² + bp) - [a(p - 1)² + b(p - 1)]

= (ap² + bp) - [a(p² + 1 - 2p) + bp - b]

= ap² + bp - ap² - a + 2ap - bp + b

= b - a + 2ap

Now, common difference = d = a_p - a_{p - 1}

= b - a + 2ap - [b - a + 2a(p - 1)]

= b - a + 2ap - b + a - 2ap + 2a

= 2a

∴ common difference = 2a

ALITER: Let S_p denotes the sum of first p terms of an AP.

Sum of first p terms = S_p = ap² + bp

Put p = 1, we get S₁ = a + b

Put p = 2, we get S₂ = 4a + 2b

Now S₁ = a₁

a₂ = S₂ - S₁

∴ a₂ = 3a + b

Now, d = a₂ - a₁

= 3a + b - (a + b)

= 2a

∴ Common difference = 2a