If ${G_1}$ and ${G_2}$ are two geometric means and $A$ the arithmetic mean inserted between two numbers, then the value of $\frac{{G_1^2}}{{{G_2}}} + \frac{{G_2^2}}{{{G_1}}}$is
$\frac{A}{2}$
$A$
$2A$
None of these
The sum of first three terms of a $G.P.$ is $\frac{13}{12}$ and their product is $-1$ Find the common ratio and the terms.
If $(y - x),\,\,2(y - a)$ and $(y - z)$ are in $H.P.$, then $x - a,$ $y - a,$ $z - a$ are in
The $5^{\text {th }}, 8^{\text {th }}$ and $11^{\text {th }}$ terms of a $G.P.$ are $p, q$ and $s,$ respectively. Show that $q^{2}=p s$
If five $G.M.’s$ are inserted between $486$ and $2/3$ then fourth $G.M.$ will be
If ${\log _a}x,\;{\log _b}x,\;{\log _c}x$ be in $H.P.$, then $a,\;b,\;c$ are in