Given: the sum of n terms of an AP is 1/2 (an^2 + bn)

To find: common difference.

Put n = 1 we get

First term = 1/2+ b

Put n = 2 we get

First term + second term = 2 × a + 2 × b

Second term = 3/2(a + b)

Therefore common difference will be

Second term – first term

Common difference = 2a