If three positive numbers a, b and c are in A.P. such that abc=8, then the minimum possible value of b is =?

1 Answer
Feb 23, 2018



For a set of positive numbers, the arithmetic mean is never smaller than the geometric mean. The geometric mean of the three numbers is #root{3}{8} = 2#. Since the numbers are in AP, their arithmetic mean is #b#. Thus the smallest possible value for #b# is 2 (this is achievable when all three numbers are 2 - an AP with zero common difference)