Question

if (k-m)^2 and k^2-m^2 are two consecutive terms of an arithmetic progression, find its arithmetic mean

Answer 1

A.M. = \(\frac{a+b}2= \frac{(k-m)^2+(k^2-m^2)}{2}\) 

= \(\frac{k^2+m^2-2km +k^2-m^2}{2}\) 

= \(\frac{2k^2-2km}{2}\)

= k² - km

= k(k-m)