If $2(y - a)$ is the $H.M.$ between $y - x$ and $y - z$,then $x - a, y - a, z - a$ are in

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

If the $A.M.$ and $H.M.$ of two numbers are $27$ and $12$ respectively,then the $G.M.$ of the two numbers will be:

If the Arithmetic Mean $(AM)$ $= 16$ and the Harmonic Mean $(HM)$ $= \frac{63}{4}$ for any two numbers,what will be the Geometric Mean $(GM)$?

Let $b_i > 1$ for $i = 1, 2, \ldots, 101$. Suppose $\log _e b_1, \log _e b_2, \ldots, \log _e b_{101}$ are in Arithmetic Progression $(A.P.)$ with the common difference $\log _e 2$. Suppose $a_1, a_2, \ldots, a_{101}$ are in $A.P.$ such that $a_1 = b_1$ and $a_{51} = b_{51}$. If $t = b_1 + b_2 + \cdots + b_{51}$ and $s = a_1 + a_2 + \cdots + a_{51}$,then:

If $a, b, c$ are in $G.P.$ and $a + x, b + x, c + x$ are in $H.P.$,then the value of $x$ is ($a, b, c$ are distinct numbers).