Which term of the $GP$ $2, 8, 32, \ldots$ is $131072$ (in $^{\text{th}}$)?

If the roots of the equation $x^3 - ax^2 + bx - c = 0$ are in $GP$,then $\frac{b^3}{a^3}$ is equal to:

Let $a_{1}, a_{2}, a_{3}, \dots$ be a $G$.$P$. of increasing positive terms such that $a_{2} \cdot a_{3} \cdot a_{4} = 64$ and $a_{1} + a_{3} + a_{5} = \frac{813}{7}$. Then $a_{3} + a_{5} + a_{7}$ is equal to:

If $a, b, c, d$ are in a geometric progression,then $(a^3 + b^3)^{-1}, (b^3 + c^3)^{-1}, (c^3 + d^3)^{-1}$ are in which progression?

Let $A_{1}, A_{2}, A_{3}, \ldots$ be squares such that for each $n \geq 1,$ the length of the side of $A_{n}$ equals the length of the diagonal of $A_{n+1}$. If the side length of $A_{1}$ is $12 \text{ cm}$,then the smallest value of $n$ for which the area of $A_{n}$ is less than $1 \text{ cm}^2$ is:

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a geometric progression are $a, b, c$ respectively,then $a^{q-r} \cdot b^{r-p} \cdot c^{p-q} = \dots\dots$