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

In an increasing geometric series,the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is $25$. Then,the sum of the $4^{\text{th}}$,$6^{\text{th}}$,and $8^{\text{th}}$ terms is equal to

If $\alpha, \beta, \gamma$ are the roots of the equation $3x^3-26x^2+52x-24=0$ such that $\alpha, \beta, \gamma$ are in geometric progression and $\alpha < \beta < \gamma$,then $3\alpha + 2\beta + \gamma =$

If $\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}$ $(x \ne 0)$,then $a, b, c, d$ are in

For a sequence $(t_n)$,if $S_n = 5(2^n - 1)$,then $t_n = \ldots$

Three numbers are in $G.P.$ such that their sum is $38$ and their product is $1728$. The greatest number among them is