If $a, b, c$ are in $G.P.$,then $\log_a x, \log_b x, \log_c x$ are in:

If $X = \sum_{n=0}^\infty a^n$,$Y = \sum_{n=0}^\infty b^n$,and $Z = \sum_{n=0}^\infty c^n$,where $a, b, c$ are in arithmetic progression and $|a| < 1, |b| < 1, |c| < 1$,then $X, Y, Z$ are in:

The numbers $log_{3}{2}, log_{6}{2}$ and $log_{12}{2}$ are in which progression?

If $\sin (\theta-\alpha), \sin \theta$ and $\sin (\theta+\alpha)$ are in $H.P.$,then the value of $\cos ^2 \theta$ is

If $x, y, z$ are in harmonic progression,then $\log(x + z) + \log(x - 2y + z) = \dots$

Let the positive numbers $a, b, c, d$ be in $A.P.$,then $abc, abd, acd, bcd$ are