If the first term of an infinite geometric series is $x$ and its sum is $5$,then which of the following is true?

If the sum of the series $1 + \frac{2}{x} + \frac{4}{x^2} + \frac{8}{x^3} + \dots \infty$ is a finite number,then

The sum of the first three terms of a $G.P.$ is $S$ and their product is $27$. Then all such $S$ lie in

Let $G_1$ and $G_2$ be the geometric means of two series $x_1, x_2, \dots, x_n$ and $y_1, y_2, \dots, y_n$ respectively. If $G$ is the geometric mean of the series $\frac{x_i}{y_i}$ where $i = 1, 2, \dots, n$,then what is $G$ equal to?

The third term of a $G$.$P$. is $9$. The product of its first five terms is

If $a, b$ and $c$ are three distinct numbers in $G.P.$ and $a + b + c = xb$,then $x$ cannot be: