If the altitudes of a triangle are in $A.P.$,then the sides of the triangle are in

If $a, b, c$ are in $A.P.$,then $2^{ax + 1}, 2^{bx + 1}, 2^{cx + 1}$ for $x \ne 0$ are in

If the ratio of the Arithmetic Mean and Harmonic Mean of two positive real numbers $a$ and $b$ is $m:n$,then find the value of $a:b$.

If $x = \sum_{n=0}^{\infty} a^{n}$,$y = \sum_{n=0}^{\infty} b^{n}$,$z = \sum_{n=0}^{\infty} c^{n}$,where $a, b, c$ are in $A.P.$ and $|a| < 1, |b| < 1, |c| < 1$,$abc \neq 0$,then:

If the ratio of $H.M.$ and $G.M.$ of two quantities is $12:13$,then the ratio of the numbers is

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