In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of its progression is equals
$\frac{{\sqrt 5 - 1}}{2}$
$\frac{{1 - \sqrt 5 }}{2}$
$1$
$2\sqrt 5 $
If ${(p + q)^{th}}$ term of a $G.P.$ be $m$ and ${(p - q)^{th}}$ term be $n$, then the ${p^{th}}$ term will be
The sum of the first $n$ terms of the series $\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{{15}}{{16}} + .........$ is
Find a $G.P.$ for which sum of the first two terms is $-4$ and the fifth term is $4$ times the third term.
Find four numbers forming a geometric progression in which the third term is greater than the first term by $9,$ and the second term is greater than the $4^{\text {th }}$ by $18 .$
In a $G.P.,$ the $3^{rd}$ term is $24$ and the $6^{\text {th }}$ term is $192 .$ Find the $10^{\text {th }}$ term.