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
G is called the geometric mean of the numbers a and b if and only if a, G, b are in GP.
G = ± √ab
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
- A.M., G.M., H.M. are in GP
- A.M > G.M > H.M