If $a,\;b,\;c$ are in $A.P.$, then ${3^a},\;{3^b},\;{3^c}$ shall be in

The $6^{th}$ term of a $G.P.$ is $32$ and its $8^{th}$ term is $128$, then the common ratio of the $G.P.$ is

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of its progression is equals

Let $a_{1}, a_{2}, a_{3}, \ldots$ be a G.P. such that $a_{1}<0$; $a_{1}+a_{2}=4$ and $a_{3}+a_{4}=16 .$ If $\sum\limits_{i=1}^{9} a_{i}=4 \lambda,$ then $\lambda$ is equal to 

If $a, b$ and $c$ be three distinct numbers in $G.P.$ and $a + b + c = xb$ then $x$ can not be

The sum of two numbers is $6$ times their geometric mean, show that numbers are in the ratio $(3+2 \sqrt{2}):(3-2 \sqrt{2})$