If $x > 1, y > 1, z > 1$ are in $G.P.$,then $\frac{1}{1 + \ln x}, \frac{1}{1 + \ln y}, \frac{1}{1 + \ln z}$ are in

Let $\alpha, \beta, \gamma$ $(\alpha < \beta < \gamma)$ be roots of $ax^3+bx^2+cx+d=0$ and $u, v, w$ $(u < v < w)$ be roots of $ak^3x^3+bk^2x^2+ckx+d=0$. If $\beta^2=\alpha \gamma$,then:

The first three terms of a geometric progression are $a, b, c$. If the harmonic mean of $a$ and $b$ is $12$ and the harmonic mean of $b$ and $c$ is $36$,then $a = \dots$

If the $4^{th}$,$7^{th}$,and $10^{th}$ terms of a Geometric Progression $(GP)$ are $a, b,$ and $c$ respectively,then:

What is the product of $n$ geometric means between $a$ and $b$?

The sum of the first four terms of a $G.P.$ is $160$ and the common ratio is $3$. Find the $4^{th}$ term.