If `S_n=n P+(n(n-1))/2Q ,w h e r eS_n` denotes the sum of the first `n` terms of an A.P., then find the common difference.

Options

A. P+Q
B. 2P+3Q
C. 2Q
D. Q

Answer

D

Explanation

Let `a_(n)` be the nth term of the A.P. Then,
`a_(n)=S_(n)-S_(n-1)`
`rArr" "a_(n)={nP+(n(n-1))/(2)Q}`
`rArr" "a_(n)=P+(n-1)Q`
`:.` Common difference `=a_(n)-a_(n-1)`
`=[P+(n-1)Q]-[P+f(n-2)Q]=Q`
ALITER Common difference `=2" (Coeff.of "n^(2))=Q`