The sum of first two terms of a $G.P.$ is $1$ and every term of this series is twice of its previous term, then the first term will be
$1/4$
$1/3$
$2/3$
$3/4$
The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is
Show that the products of the corresponding terms of the sequences $a,$ $ar,$ $a r^{2},$ $......a r^{n-1}$ and $A, A R, A R^{2}, \ldots, A R^{n-1}$ form a $G .P.,$ and find the common ratio.
A $G.P.$ consists of an even number of terms. If the sum of all the terms is $5$ times the sum of the terms occupying odd places, then the common ratio will be equal to
If the sum of the series $1 + \frac{2}{x} + \frac{4}{{{x^2}}} + \frac{8}{{{x^3}}} + ....\infty $ is a finite number, then
${7^{th}}$ term of the sequence $\sqrt 2 ,\;\sqrt {10} ,\;5\sqrt 2 ,\;.......$ is