If $a,\,b,\,c$ are in $G.P.$, then
$a({b^2} + {a^2}) = c({b^2} + {c^2})$
$a({b^2} + {c^2}) = c({a^2} + {b^2})$
${a^2}(b + c) = {c^2}(a + b)$
None of these
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 in a $G.P.$ of $64$ terms, the sum of all the terms is $7$ times the sum of the odd terms of the $G.P,$ then the common ratio of the $G.P$. is equal to
The $G.M.$ of the numbers $3,\,{3^2},\,{3^3},....,\,{3^n}$ is
The number of bacteria in a certain culture doubles every hour. If there were $30$ bacteria present in the culture originally, how many bacteria will be present at the end of $2^{\text {nd }}$ hour, $4^{\text {th }}$ hour and $n^{\text {th }}$ hour $?$
If $a,b,c$ are in $A.P.$, then ${2^{ax + 1}},{2^{bx + 1}},\,{2^{cx + 1}},x \ne 0$ are in