The first term of a harmonic progression is $1/7$ and the second term is $1/9$. The $12^{th}$ term is

$A$ boy goes from his home to school at a speed of $x \text{ km/hr}$ and returns at a speed of $y \text{ km/hr}$. What is the average speed of the boy?

If $\cos \left(x-\frac{\pi}{3}\right), \cos x, \cos \left(x+\frac{\pi}{3}\right)$ are in a harmonic progression,then $\cos x=$

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 which progression?

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

If $a, b, c, d$ are in $H.P.$,then $ab + bc + cd$ is equal to