Question

The common difference of an A.P., the sum of whose n terms is S_n, is 

A. S_n – 2S_n–1 + S_n–2 

B. S_{n – 2}S_n–1– S_n–2 

C. S_n – S_n–2 

D. S_n – S_n–1

Answer 1

a_n is the n^th term of an A.P and a_n–1 is the (n–1)^th term of an A.P, 

d = common difference, 

S_n = sum of n terms of an A.P 

d= a_n – a_n–1 

But a_n= S_n – S_n–1 

And a_n–1= S_n–1 – S_n–2 

So d= S_n – S_n–1 – (S_n–1 – S_n–2) 

d= S_{n – 2} S_n–1 + S_n–2