The geometric and harmonic means of two numbers $x_1$ and $x_2$ are $18$ and $16\frac{8}{13}$ respectively. The value of $|x_1 - x_2|$ is

Let ${a_1, a_2, \dots, a_{10}}$ be in $A.P.$ and ${h_1, h_2, \dots, h_{10}}$ be in $H.P.$ If ${a_1 = h_1 = 2}$ and ${a_{10} = h_{10} = 3}$,then the value of ${a_4 h_7}$ is:

If the arithmetic,geometric and harmonic means between two positive real numbers be $A, G$ and $H$,then

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

In a $G.P.$,the sum of three numbers is $14$. If $1$ is added to the first two numbers and subtracted from the third number,the series becomes an $A.P.$. Then,the greatest number is:

If $a, b, c$ are in $G.P.$ and $a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}} = k,$ prove that $x, y, z$ are in $A.P.$