If $a, b, c$ are in $A.P.$ and $b, c, d$ are in $H.P.$,then

If the arithmetic,geometric,and harmonic means between two distinct positive real numbers are $A, G,$ and $H$ respectively,then the relation between them is

The difference between two numbers is $48$ and the difference between their arithmetic mean and geometric mean is $18$. The larger of the two numbers is:

Let $0 < z < y < x$ be three real numbers such that $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in an arithmetic progression and $x, \sqrt{2}y, z$ are in a geometric progression. If $xy + yz + zx = \frac{3}{\sqrt{2}} xyz$,then $3(x + y + z)^2$ is equal to $............$.

If $a, b,$ and $c$ are in arithmetic progression,then $2^{ax + 1}, 2^{bx + 1},$ and $2^{cx + 1}$ for $x \neq 0$ are...

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