If the sum of n terms of an A.P. is nP + 1/2 n(n - 1)Q where P and Q a

1.	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» 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

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»

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