Question

if S_n = nP + 1/2n(n-1)Q where S_n denotes the sum of the first n terms of an AP then the common difference is.

Answer 1

Dear student,

put n=1 in,
$$\begin{gathered} S_n=nP+\frac{1}{2}n(n-1)Q \\ {S}_1=P \\ n=2,S_2=2P+Q \end{gathered}$$
first term of the AP = S₁ = P
second term, S₂-S₁=2P+Q-P = P+Q
common difference d= second term -first term = P+Q-P= Q