Question

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

Answer 1

2

Explanation:

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)