Question

If the sum of ‘n’ terms of an A.P.is (pn + qn²), where p and q are constant find the common difference.

Answer 1

Given S_n = pn + qn²  ………………(1) 

Substituting n = 1, 2, we get 

S₁ = p(1) + q(1)²  = p + q and 

S₂ =p(2) + q(2)²  =2p + 4q 

we know that, S₁ = a = first term and S₂ = first term + second term = a + (a + d), 

where d = C.D. 

S₂ = 2a + d = 2p + 4q = 2 (p + q) + d = 2p + 2q + d 

= d = 2p + 4q - 2p - 2q = 2q