Three non-zero real numbers form an $A.P.$ and the squares of these numbers taken in the same order form a $G.P.$ Then the number of all possible common ratios of the $G.P.$ is
$1$
$2$
$3$
None of these
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 $a,\;b,\;c$ are in $G.P.$ and $x,\,y$ are the arithmetic means between $a,\;b$ and $b,\;c$ respectively, then $\frac{a}{x} + \frac{c}{y}$ is equal to
If the first and ${(2n - 1)^{th}}$ terms of an $A.P., G.P.$ and $H.P.$ are equal and their ${n^{th}}$ terms are respectively $a,\;b$ and $c$, then
If $a,\;b,\;c$ are in $G.P.$, $a - b,\;c - a,\;b - c$ are in $H.P.$, then $a + 4b + c$ is equal to
Let $3, a, b, c$ be in $A.P.$ and $3, a-1, b+1, c+9$ be in $G.P.$ Then, the arithmetic mean of $a, b$ and $c$ is :