If the geometric mean between two numbers is $4$ and the arithmetic mean is $5$,then the harmonic mean is .......

The product of $n$ positive numbers is $1$. The sum of these numbers cannot be less than what value?

If the Arithmetic Mean of $a$ and $b$ is $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$,then $n = \dots$

If $a, b, c$ are any three positive numbers,then what is the minimum value of $(a + b + c) \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$?

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 $p^{\text{th}}, q^{\text{th}}, r^{\text{th}},$ and $s^{\text{th}}$ terms of an $A.P.$ are in $G.P.,$ then show that $(p-q), (q-r),$ and $(r-s)$ are also in $G.P.$