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Question: If \(S _ { n } = n P + \frac { 1 } { 2 } n ( n - 1 ) Q\) , where \(S _ { n }\) denotes the sum of t...

If Sn=nP+12n(n−1)QS _ { n } = n P + \frac { 1 } { 2 } n ( n - 1 ) Q , where SnS _ { n } denotes the sum of the first nn terms of an A.P., then the common difference is.

A

P+QP + Q

B

2P+3Q2 P + 3 Q

C

2Q2 Q

D

QQ

Answer

QQ

Explanation

Solution

ObviouslySn=n2{2P+(n−1)Q}S _ { n } = \frac { n } { 2 } \{ 2 P + ( n - 1 ) Q \}, hence

d=Qd = Q.

Aliter : d=T2−T1d = T _ { 2 } - T _ { 1 } =(S2−S1)−S1= \left( S _ { 2 } - S _ { 1 } \right) - S _ { 1 }