Question

Write the common difference of an A.P. the sum of whose first n terms is P/2 n² + Qn.

Answer 1

Here,

S_n = P/2 n² + Qn

Now, 

Common difference of A.P. is given by d = t₂ - t₁

Answer 2

We know that,

Sn​=2n​[2a+(n−1)d]   ....(i)

Sn​=2P​n2+Qn  

Sn​=2n​(2Q+Pn)

Sn​=2n​(2Q+P(n−1)+P)

Sn​=2n​(2(Q+2P​)+P(n−1))    ....(ii)

Comparing (i) and (ii) we get,

a=(Q+2P​)

d=P

Hence, common difference, d=P