Three harmonic means `H_(1),H_(2),H_(3)` are inserted between the two numbers 20 and 4. Then find `H_(1),H_(2)` and `H_(3)`.

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 .

If A_(1),A_(2) are between two numbers, then (A_(1)+A_(2))/(H_(1)+H_(2)) is equal to

Three horses H_(1), H_(2) and H_(3) are in a race which i s won by one o f them. If H_(1) is twice as likely to win as H_(2) and H_(2) is twice as likely to win as H_(3) , then their res p ective pro b abilities of Winnig are .

If 8 harmonic means are inserted between two numbes a and b (altb) such that arithmetic mean of a and b is 5/4 times equal to geometric mean of a and b then ((H_(8)-a)/(b-H_(8))) is equal to

Let a_(1), a_(2) ...be positive real numbers in geometric progression. For n, if A_(n), G_(n), H_(n) are respectively the arithmetic mean, geometric mean and harmonic mean of a_(1), a_(2),..., a_(n) . Then, find an expression for the geometric mean of G_(1), G_(2),...,G_(n) in terms of A_(1), A_(2),...,A_(n), H_(1), H_(2),..., H_(n)

If H_1.,H_2,…,H_20 are 20 harmonic means between 2 and 3, then (H_1+2)/(H_1-2)+(H_20+3)/(H_20-3)=

If 2, h_(1), h_(2),………,h_(20)6 are in harmonic progression and 2, a_(1),a_(2),……..,a_(20), 6 are in arithmetic progression, then the value of a_(3)h_(18) is equal to

The numbers h_(1),h_(2),h_(3),h_(4),...,h_(10) are in harmonicprogression and a_(1),a_(2),...,a_(10) are in arithmetic progression.If a_(1)=h_(1)=3 and a_(7)=h_(7)=39, thenthe value of a_(4)xx h_(4) is