If $a$ and $b$ are two different positive real numbers,then which of the following relations is true?

If $A.M.$ and $G.M.$ of two positive numbers $a$ and $b$ are $10$ and $8$ respectively,find the numbers.

If the arithmetic and geometric means of $a$ and $b$ are $A$ and $G$ respectively,then the value of $A - G$ is

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 arithmetic mean of two numbers is $A$ and the geometric mean is $G$,then the numbers are

Given a sequence of $4$ numbers,the first three of which are in $G.P.$ and the last three are in $A.P.$ with a common difference of $6$. If the first and last terms in this sequence are equal,then the last term is: