If $a$ be the arithmetic mean of $b$ and $c$ and ${G_1},\;{G_2}$ be the two geometric means between them, then $G_1^3 + G_2^3 = $

If $a, b, c$ are in $GP$ and $4a, 5b, 4c$ are in $AP$ such that $a + b + c = 70$,  then value of $a^3 + b^3 + c^3$ is

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

If the $A.M., G.M.$ and $H.M.$ between two positive numbers $a$ and $b$ are equal, then

If $a,\;b,\;c$ are in $G.P.$ and $\log a - \log 2b,\;\log 2b - \log 3c$ and $\log 3c - \log a$ are in $A.P.$, then $a,\;b,\;c$ are the length of the sides of a triangle which is

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