If $a,\;b,\;c$ be in $A.P.$ and $b,\;c,\;d$ be in $H.P.$, then

Let $A_1$ and $A_2$ be two arithmetic means and $G_1, G_2$, $G _3$ be three geometric means of two distinct positive numbers. The $G _1^4+ G _2^4+ G _3^4+ G _1^2 G _3^2$ is equal to

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

If the arithmetic mean of two numbers be $A$ and geometric mean be $G$, then the numbers will be

$a,\,g,\,h$ are arithmetic mean, geometric mean and harmonic mean between two positive numbers $x$ and $y$ respectively. Then identify the correct statement among the following

The common difference of an $A.P.$ whose first term is unity and whose second, tenth and thirty fourth terms are in $G.P.$, is