Question

prove that the sum of n terms of am between a & b is n times the am between a & b

Answer 1

Let A 1, A 2 ........ An be n A.M. between two numbers a and b

Then a, A 1, A 2 ..... An , b is in A.P. with

Common difference (d) = (b-a)/(n+1)

So,
A1+ A2+ .........An= n/2(A1+An)
= n/2(A1-d+An+d)
= n/2(a+b)
= n* (a+b)/2