If the ratio of two numbers is $9:1$,then the ratio of their geometric mean to their harmonic mean is

If $A$ and $G$ are the arithmetic mean and geometric mean of $a$ and $b$ respectively,then what is the value of $A - G$?

If $a, b, c$ are in $G.P.$ and $a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}} = k,$ prove that $x, y, z$ are in $A.P.$

Let the first three terms $2, p$ and $q$,with $q \neq 2$,of a $G.P.$ be respectively the $7^{\text{th}}$,$8^{\text{th}}$ and $13^{\text{th}}$ terms of an $A.P.$ If the $5^{\text{th}}$ term of the $G.P.$ is the $n^{\text{th}}$ term of the $A.P.$,then $n$ is equal to

If $A, G,$ and $H$ are the arithmetic mean,geometric mean,and harmonic mean of two given numbers respectively,then which of the following is true?

If the arithmetic and geometric means of $a$ and $b$ are $A$ and $G$ respectively,then the value of $A - G$ is