Let`A_(1),G_(1),H_(1)` denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For `nge2`, let `A_(n-1),G_(n-1)" and "H_(n-1)` has arithmetic,geometric and harmonic means as `A_(n),G_(n),H_(n)` respectively.
Which of the following statement is correct?

Let A_1 , G_1, H_1 denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For n >2, let A_(n-1),G_(n-1) and H_(n-1) has arithmetic, geometric and harmonic means as A_n, G_N, H_N, respectively.

If A_1, A_2, G_1, G_2, ; a n dH_1, H_2 are two arithmetic, geometric and harmonic means respectively, between two quantities aa n db ,t h e na b is equal to A_1H_2 b. A_2H_1 c. G_1G_2 d. none of these

If A_(1) , A_(2) , A_(3) , G_(1) , G_(2) , G_(3) , and H_(1) , H_(2) , H_(3) are the three arithmetic, geometric and harmonic means between two positive numbers a and b(a gt b) , then which of the following is/are true ?

If H_(1) and H_(2) are two harmonic means between two positive numbers a and b (a != b) , A and G are the arithmetic and geometric menas between a and b , then (H_(2)+H_(1))/(H_(2)H_(1)) is

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 arithmetic mean of two positive numbers is A, their geometric mean is G and harmonic mean H, then H is equal to

The arithmetic mean of two positive numbers is 6 and their geometric mean G and harmonic mean H satisfy the relation G^(2)+3H=48 . Then the product of the two numbers is

Let alpha and beta be two positive real numbers. Suppose A_1, A_2 are two arithmetic means; G_1 ,G_2 are tow geometrie means and H_1 H_2 are two harmonic means between alpha and beta , then

If A_(1),A_(2),A_(3) denote respectively the areas of an inscribed polygon of 2n sides , inscribed polygon of n sides and circumscribed poylgon of n sides ,then A_(1),A_(2),A_(3) are in

Let there be a GP whose first term is a and the common ratio is r. If A and H are the arithmetic mean and harmonic mean respectively for the first n terms of the G P, AH is equal to