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.