Let three real numbers $a, b, c$ be in arithmetic progression and $\mathrm{a}+1, \mathrm{~b}, \mathrm{c}+3$ be in geometric progression. If $\mathrm{a}>10$ and the arithmetic mean of $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ is $8$ , then the cube of the geometric mean of $a, b$ and $c$ is

If $a,\;b,\;c$ are in $H.P.$, then for all $n \in N$ the true statement is

If $a,\;b,\,c$ be in $G.P.$ and $a + x,\;b + x,\;c + x$ in $H.P.$, then the value of $x$ is ($a,\;b,\;c$ are distinct numbers)

If the $2^{nd}\,, \,5^{th}\,\, and \,\,9^{th}$ terms of a non-constant $A.P.$ are in $G.P.$, then the common ratio of this $G.P.$ is :

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

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