If the sum of n terms of an AP is , where P and Q are constants then find the common difference.

Let the first term be a and common difference be d


To Find: d


Given: Sum of n terms of AP =



2a + (n - 1)d = 2P + (n - 1)Q
2(a - P) = (n - 1)(Q - d)
Put n = 1 to get the first term as sum of 1 term of an AP is the term itself.


P = a
(n - 1)(Q - d) = 0
For n not equal to 1 Q = d


Common difference is Q.


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