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

If $b + c, c + a, a + b$ are in $H.P.$,then $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}$ are in

If for the harmonic progression,$t_{7} = \frac{1}{10}$ and $t_{12} = \frac{1}{25}$,then $t_{20} =$

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 . . . . progression.

If $\tan B = \frac{2 \sin A \sin C}{\sin (A+C)}$,then $\tan A, \tan B$ and $\tan C$ are in

If $\cos (\theta-\alpha), \cos \theta$ and $\cos (\theta+\alpha)$ are in harmonic progression,then $2 \tan ^2 \theta=$