Which term of the following sequence: $\sqrt{3}, 3, 3\sqrt{3}, \ldots$ is $729$ (in $^{\text{th}}$)?

For $0 < \phi < \frac{\pi}{2}$,if $x = \sum_{n=0}^\infty \cos^{2n}\phi$,$y = \sum_{n=0}^\infty \sin^{2n}\phi$,and $z = \sum_{n=0}^\infty \cos^{2n}\phi \sin^{2n}\phi$,then:

If $A, B, C$ are the $p^{th}, q^{th},$ and $r^{th}$ terms of a $GP$ respectively,then $A^{q-r} \cdot B^{r-p} \cdot C^{p-q} =$

Let $a_1, a_2, ..., a_{10}$ be a $G.P.$ If $\frac{a_3}{a_1} = 25$,then $\frac{a_9}{a_5}$ is equal to:

If the roots of the equation $3x^3-26x^2+52x-24=0$ are in geometric progression,then the sum of two of its roots 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 equal to: