Let `n in N ,n > 25.` Let `A ,G ,H` deonote te arithmetic mean, geometric mean, and harmonic mean of 25 and `ndot` The least value of `n` for which `A ,G ,H in {25 , 26 , n}` is a. 49 b. 81 c.169 d. 225

If H is the harmonic mean between Pa n dQ then find the value of H//P+H//Qdot

.Let a_1, a_2,............ be positive real numbers in geometric progression. For each n, let A_n G_n, H_n , be respectively the arithmetic mean, geometric mean & harmonic mean of a_1,a_2..........a_n . 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 .

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)

Find the least value of n such that (n-2)x^2+8x+n+4>0,AAx in R ,w h e r en in Ndot

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

Let A;G;H be the arithmetic; geometric and harmonic means between three given no. a;b;c then the equation having a;b;c as its root is x^3-3Ax^2+3G^3/H x-G^3=0

If are the n Arithmetic means between a and b , then 2sum_(I - 1)^(n)a_(i) =

If 9^7+7^9 is divisible b 2^n , then find the greatest value of n ,w h e r en in Ndot

If (a^(n + 1) + b^(n + 1))/(a^(n) + b^(n)) is the arithmetic mean between a and b , then n =

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.