Means of Progressions

Arithmetic Mean

A is called the arithmetic mean of the numbers a and b if and only if a, A, b are in AP.

A − a = b − A

2A = a + b

A = (a+b)/2

Geometric Mean

G is called the geometric mean of the numbers a and b if and only if a, G, b are in GP.

G = ± √ab

Harmonic Mean

H is called the harmonic mean between a and b if a, H, b are in HP.

H = 2ab/(a+b)

Relation between A.M., G.M. and H.M.

If a, b are two different positive numbers then

1. A.M., G.M., H.M. are in GP
2. A.M > G.M > H.M