If the $p^{th}, q^{th}, r^{th}$ and $s^{th}$ terms of an $A.P.$ are in $G.P.$,then $(p - q), (q - r), (r - s)$ will be in:

If $a, x, y, z, b$ are in Arithmetic Progression ($A$.$P$.) such that $x + y + z = 15$,and if $a, x, y, z, b$ are in Harmonic Progression ($H$.$P$.) such that $1/x + 1/y + 1/z = 5/3$,find the values of $a$ and $b$.

If $a, b, c$ are in $A.P.$ and $a^2, b^2, c^2$ are in $G.P.$ such that $a < b < c$ and $a+b+c = \frac{3}{4}$,then the value of $a$ is

If $p$ and $q$ are two arithmetic means between two numbers and $G$ is the geometric mean between them,then $G^2 = \dots \dots$.

Given an $A.P.$ and a $G.P.$ with positive terms,where the first and second terms of both progressions are equal. If $a_n$ and $b_n$ are the $n^{\text{th}}$ terms of the $A.P.$ and $G.P.$ respectively,then:

If the ratio of $H.M.$ and $G.M.$ between two numbers $a$ and $b$ is $4:5$,then the ratio of the two numbers will be