The value of $n$ for which $\frac{x^{n+1}+y^{n+1}}{x^{n}+y^{n}}$ is the geometric mean of $x$ and $y$ is

If the $p^{th}, q^{th}, r^{th}$ and $s^{th}$ terms of an $A.P.$ are in $G.P.$,then $(p - q), (q - r), (r - s)$ will be in:

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

Let ${a_1, a_2, \dots, a_{10}}$ be in $A.P.$ and ${h_1, h_2, \dots, h_{10}}$ be in $H.P.$ If ${a_1 = h_1 = 2}$ and ${a_{10} = h_{10} = 3}$,then the value of ${a_4 h_7}$ is:

If $A$,$G$,and $H$ are the arithmetic,geometric,and harmonic means between two positive real numbers,respectively,then:

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