If every term of a $G.P.$ with positive terms is the sum of its two previous terms, then the common ratio of the series is
$1$
$\frac{2}{{\sqrt 5 }}$
$\frac{{\sqrt 5 - 1}}{2}$
$\frac{{\sqrt 5 + 1}}{2}$
The third term of a $G.P.$ is the square of first term. If the second term is $8$, then the ${6^{th}}$ term is
If $1\, + \,\sin x\, + \,{\sin ^2}x\, + \,...\infty \, = \,4\, + \,2\sqrt 3 ,\,0\, < \,x\, < \,\pi $ then
Suppose the sides of a triangle form a geometric progression with common ratio $r$. Then, $r$ lies in the interval
If the first term of a $G.P. a_1, a_2, a_3......$ is unity such that $4a_2 + 5a_3$ is least, then the common ratio of $G.P.$ is
Let $a, a r, a r^2, \ldots . . .$. be an infinite $G.P.$ If $\sum_{n=0}^{\infty} a^n=57$ and $\sum_{n=0}^{\infty} a^3 r^{3 n}=9747$, then $a+18 r$ is equal to :