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:

If ${x^a} = {x^{b/2}}{z^{b/2}} = {z^c}$,then $a, b, c$ are in

When $\frac{1}{a} + \frac{1}{c} + \frac{1}{a - b} + \frac{1}{c - b} = 0$ and $b \ne a \ne c$,then $a, b, c$ are

If $\frac{a^{n + 1} + b^{n + 1}}{a^n + b^n}$ is the harmonic mean between $a$ and $b$,then the value of $n$ is

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

The harmonic mean of $3, 7, 8, 10, 14$ is