If ${A_1},\;{A_2};{G_1},\;{G_2}$ and ${H_1},\;{H_2}$ be $AM's,\;GM's$ and $HM's$ between two quantities, then the value of $\frac{{{G_1}{G_2}}}{{{H_1}{H_2}}}$ is
$\frac{{{A_1} + {A_2}}}{{{H_1} + {H_2}}}$
$\frac{{{A_1} - {A_2}}}{{{H_1} + {H_2}}}$
$\frac{{{A_1} + {A_2}}}{{{H_1} - {H_2}}}$
$\frac{{{A_1} - {A_2}}}{{{H_1} - {H_2}}}$
If $a,\;b,\;c$ are in $A.P.$, then $\frac{a}{{bc}},\;\frac{1}{c},\;\frac{2}{b}$ are in
If $\frac{{a + bx}}{{a - bx}} = \frac{{b + cx}}{{b - cx}} = \frac{{c + dx}}{{c - dx}}(x \ne 0)$, then $a,\;b,\;c,\;d$ are in
If the first and ${(2n - 1)^{th}}$ terms of an $A.P., G.P.$ and $H.P.$ are equal and their ${n^{th}}$ terms are respectively $a,\;b$ and $c$, then
If $n$ arithmetic means $a_1,a_2,......a_n$ are inserted between $50$ and $100$ and $n$ harmonic means $h_1$ , $h_2$ , ...... $h_n$ are inserted between the same two numbers, then $a_2h_{n-1}$ is equal to
If $m$ is the $A.M$ of two distinct real numbers $ l$ and $n (l,n>1) $ and $G_1, G_2$ and $G_3$ are three geometric means between $l$ and $n$ then $G_1^4 + 2G_2^4 + G_3^4$ equals :