Insertion of n HM between two numbers

Insertion of GM between two numbers

If sum of A.M. and H.M between two numbers is 25 and their GM is,then sum of two numbers

If the ratio of H.M. and G.M. between two numbers a and b is 4:5, then find the ratio of the two number?

The AM, HM and GM between two numbers are (144)/(15), 15 and 12, but not necessarily in this order then, HM, GM and AM respectively are :

The AM, HM and GM between two number are (144)/(15) , 15 and 12, but not necessarily in this order then, HM, GM and AM respectively are

If n A.Ms are inserted between two numbers, prove that the sum of the means equidistant from the beginning and the end is constant.

Two AMs. A_1 and A_2 , two GMs. G_1 and G_2 and two HMs. H_1 and H_2 are inserted between any two numbers. Then find the arithmetic mean between H_1 and H_2 in terms of A_1, A_2, G_1, G_2 .