# Relationship Between Arithmetic Mean, Harmonic Mean, and Geometric Mean of Two Numbers

For two numbers x and y, let x, a, y be a sequence of three numbers. If x, a, y is an arithmetic progression then 'a' is called *arithmetic mean*. If x, a, y is a geometric progression then 'a' is called *geometric mean*. If x, a, y form a harmonic progression then 'a' is called *harmonic mean*.

Let AM = arithmetic mean, GM = geometric mean, and HM = harmonic mean. The relationship between the three is given by the formula

Below is the derivation of this relationship.