If the $A.M.$ and $H.M.$ of two numbers are $27$ and $12$ respectively,then the $G.M.$ of the two numbers will be:

If the arithmetic mean of two numbers $a$ and $b$,where $a > b > 0$,is five times their geometric mean,then $\frac{a + b}{a - b}$ is equal to

Let $A_1, G_1, H_1$ be the arithmetic,geometric,and harmonic means of two distinct positive numbers. For $n \geq 2$,let $A_n, G_n, H_n$ be the arithmetic,geometric,and harmonic means of $A_{n-1}$ and $H_{n-1}$ respectively. Which of the following statements is true?

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 the $A.M.$ is twice the $G.M.$ of the numbers $a$ and $b$,then $a:b$ will be

If $9$ arithmetic means $(A.M.s)$ and $9$ harmonic means $(H.M.s)$ are inserted between $2$ and $3$,and if the harmonic mean $H$ corresponds to the arithmetic mean $A$ (i.e.,the $j^{th}$ $A.M.$ and $j^{th}$ $H.M.$),then $A + \frac{6}{H} = $