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

If the arithmetic mean of two numbers is $A$ and the geometric mean is $G$,then 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 first and $(2n-1)$-th terms of an $AP$, $GP$, and $HP$ are equal and their $n$-th terms are respectively $a, b, c$, then always

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} = $

If the arithmetic mean between $p$ and $q$ $(p > q)$ is twice the geometric mean,then $p : q = .......$