Let $a$ and $b$ be roots of ${x^2} - 3x + p = 0$ and let $c$ and $d$ be the roots of ${x^2} - 12x + q = 0$, where $a,\;b,\;c,\;d$ form an increasing G.P. Then the ratio of $(q + p):(q - p)$ is equal to
$8 : 7$
$11 : 10$
$17 : 15$
None of these
The roots of the equation
$x^5 - 40x^4 + px^3 + qx^2 + rx + s = 0$ are in $G.P.$ The sum of their reciprocals is $10$. Then the value of $\left| s \right|$ is
If the ${5^{th}}$ term of a $G.P.$ is $\frac{1}{3}$ and ${9^{th}}$ term is $\frac{{16}}{{243}}$, then the ${4^{th}}$ term will be
Find the $10^{\text {th }}$ and $n^{\text {th }}$ terms of the $G.P.$ $5,25,125, \ldots$
If the ${10^{th}}$ term of a geometric progression is $9$ and ${4^{th}}$ term is $4$, then its ${7^{th}}$ term is
Show that the ratio of the sum of first $n$ terms of a $G.P.$ to the sum of terms from
$(n+1)^{ th }$ to $(2 n)^{ th }$ term is $\frac{1}{r^{n}}$