Q24 of 202 Page 10

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

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

If are in A.P. Then, x =

The nth term of an A.P., the sum of whose n terms is S_n, is

If the sums of n terms of two arithmetic progressions are in the ratio , then their nth terms are in the ratio

If S_n, denote the sum of n terms of an A.P. with first term a and common difference d such that , is independent of x, then

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