Question

If the sum of n terms of an A.P. is nP + 1/2 n(n - 1)Q where P and Q are constants, find the common difference.

Answer 1

It is given that sum of n terms of AP is nP + 1/2 n(n-1)Q

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