If ${a_1}, {a_2}, {a_3}, \dots, {a_n}$ are in $H.P.$,then the expression ${a_1}{a_2} + {a_2}{a_3} + \dots + {a_{n - 1}}{a_n}$ is equal to:

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 ....... $\text{mph}$.

Let $a_1, a_2, a_3, \dots$ be a harmonic progression where $a_1 = 5$ and $a_{20} = 25$. What is the smallest positive integer $n$ such that $a_n < 0$?

If $a, b, c$ are in $H.P.$,then

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

The sixth $H.M.$ between $3$ and $\frac{6}{13}$ is