Question

If the sum of n terms of an AP is { + 1/2 ( − 1)}, where P and Q are constants then find the common difference.

Answer 1

Let the first term be a and common difference be d

To Find: d

⇒ 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.