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

If $\alpha, \beta, \gamma$ are the geometric means between $ca, ab$; $ab, bc$; and $bc, ca$ respectively,where $a, b, c$ are in $A.P.$,then $\alpha^2, \beta^2, \gamma^2$ are in

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

If $7$ times the $7^{th}$ term of an $A.P.$ is equal to $11$ times its $11^{th}$ term,then the $18^{th}$ term of the $A.P.$ is

If $a, b, c$ are the $p^{th}, q^{th}$ and $r^{th}$ terms of a $G.P.$,then $\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q$ is equal to

If $p$ times the $p^{th}$ term of an $A.P.$ is equal to $q$ times the $q^{th}$ term of an $A.P.$,then the $(p + q)^{th}$ term is