If $A.M.$ of two terms is $9$ and $H.M.$ is $36$,then $G.M.$ will be

If the arithmetic mean of two numbers $a$ and $b$ is twice their geometric mean,then $a : b = \dots$

Three positive numbers form an increasing $G.P.$ If the middle term in this $G.P.$ is doubled,the new numbers are in $A.P.$ Then the common ratio of the $G.P.$ is:

The Geometric Mean $(G.M.)$ and Harmonic Mean $(H.M.)$ of two numbers are $10$ and $8$ respectively. The numbers are:

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 $G.P.$

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