Find the harmonic mean of $a/b$ and $b/a$.

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 $7^{th}$ term of a $H.P.$ is $\frac{1}{10}$ and the $12^{th}$ term is $\frac{1}{25}$,then the $20^{th}$ term is

If $(y - x)$,$2(y - a)$,and $(y - z)$ are in $H.P.$,then $(x - a)$,$(y - a)$,and $(z - a)$ are in

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:

If the $7^{th}$ term of a harmonic progression is $8$ and the $8^{th}$ term is $7$,then its $15^{th}$ term is