Question: If S<sub>n</sub>= nP +<img src="https://cdn.pureessence.tech/canvas_532.png?top_left_x=600&top_left_...

Question

If S_n= nP +(n – 1)Q, where S_n denotes the sum of the first n terms of an A.P. then the common difference is –

Answer 1

Solution

S_n = nP + $\frac { \mathrm { n } ^ { 2 } \mathrm { Q } } { 2 }$ – $\frac { \mathrm { nQ } } { 2 }$ = $\frac { \mathrm { n } ^ { 2 } \mathrm { Q } } { 2 }$ + n(P – $\frac { \mathrm { Q } } { 2 }$ )

As S_n is of the form An² + Bn with c.d = 2A

\ Here d = 2(Q/2) = Q