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 the $A.M.$ is twice the $G.M.$ of the numbers $a$ and $b$,then $a:b$ will be

Given a sequence of $4$ numbers,the first three of which are in $G.P.$ and the last three are in $A.P.$ with a common difference of $6$. If the first and last terms in this sequence are equal,then the last term is:

The Geometric Mean $(G.M.)$ and Harmonic Mean $(H.M.)$ of two numbers are $10$ and $8$ respectively. The numbers are:

The arithmetic mean and the geometric mean of two distinct $2$-digit numbers $x$ and $y$ are two integers,one of which can be obtained by reversing the digits of the other (in base $10$ representation). Then,$x+y$ equals

Let the first three terms $2, p$ and $q$,with $q \neq 2$,of a $G.P.$ be respectively the $7^{\text{th}}$,$8^{\text{th}}$ and $13^{\text{th}}$ terms of an $A.P.$ If the $5^{\text{th}}$ term of the $G.P.$ is the $n^{\text{th}}$ term of the $A.P.$,then $n$ is equal to