Question

If the nth term of a progression be a linear expression in n then prove that this progression is an AP (plz give an appropriate ans..)

Answer 1

if the nth term is linear in n then ,

let

Tn=an+b⇒Tn−Tn−1=(an+b)−(a(n−1)+b)=a[Constant]as we know in arithmetic progression Tn−Tn−1 is common difference which is constant here so we can say it is the nth term of an A.P having common difference =a and first term T1=a+b