If the sum of n terms of an A.P. is nP + n(n - 1)Q where P and Q are constants, find the common difference.

it is given that sum of n terms of AP is

To find: the common difference


Substituting n = 1 gives the sum of the first term, that is the first term itself


a1 = P


Substituting n = 2 gives the sum of first two terms


a1 + a2 = 2P + Q


a2 = P + Q


Now common difference d = a2 - a1 = Q


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