If $a, b, c$ are in harmonic progression,then $\frac{a-b}{b-c} = \dots$

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 $a, b, c$ are in $G$.$P$. $(a > 1, b > 1, c > 1)$, then for any real number $x$ $(x > 0, x \neq 1)$, the terms $\log_{a} x, \log_{b} x, \log_{c} x$ are in:

Five numbers are in $HP$. The middle term is $1$ and the ratio of the second and the fourth terms is $2:1$. Then, the sum of the first three terms is

If $a, b, c$ are in $G.P.$,then $\log_a x, \log_b x, \log_c x$ 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 ....... $\text{mph}$.