Question

If a,b,c,d,e and f are in AP then express e-c in terms of d-c

Answer 1

We have given a,b,c,d,e,f are in A.P

So, let common difference = x

so, a+x=b

a+2x=c

a+3x = d

a+4x = e

a+5x = f

=> e-c = a+4x-a-2x = 2x ---------(1)

=> d-c = a+3x-a-2x = x --------(2)

so from 1 and 2 we get

e-c = 2(d-c)