The geometric mean of two numbers is $6$ and their arithmetic mean is $6.5$. The numbers are

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 ${G_1}$ and ${G_2}$ are two geometric means and $A$ is the arithmetic mean inserted between two numbers,then the value of $\frac{{G_1^2}}{{{G_2}}} + \frac{{G_2^2}}{{{G_1}}}$ is

For what value of $m$ is $\frac{a^{m+1}+b^{m+1}}{a^{m}+b^{m}}$ the arithmetic mean of $a$ and $b$?

If $a, b,$ and $c$ are in arithmetic progression,then $2^{ax + 1}, 2^{bx + 1},$ and $2^{cx + 1}$ for $x \neq 0$ are...

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