Which number should be added to the numbers $13, 15, 19$ so that the resulting numbers are the consecutive terms of a $H.P.$?

If the $5^{th}$ term of a Harmonic Progression $(H.P.)$ is $1/45$ and the $11^{th}$ term is $1/69$,then its $16^{th}$ term is...

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.

Find the $9^{th}$ term of the series $\frac{1}{7} + \frac{1}{14} + \frac{1}{21} + \frac{1}{28} + \dots$

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

An aeroplane flies around a square,the sides of which measure $100$ miles each. The aeroplane covers the first side at a speed of $100 \text{ mph}$,the second side at $200 \text{ mph}$,the third side at $300 \text{ mph}$,and the fourth side at $400 \text{ mph}$. The average speed of the aeroplane around the square is ....... $\text{mph}$.