The sum of a few terms of a geometric series is $728$. If the common ratio is $3$ and the last term is $486$,then the first term of the series will be:

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 equal to:

If $a = r + r^2 + r^3 + \dots + \infty$,then the value of $r$ is .......

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

If $x > 1, y > 1, z > 1$ are in $G.P.$,then $\frac{1}{1 + \ln x}, \frac{1}{1 + \ln y}, \frac{1}{1 + \ln z}$ are in

The arithmetic mean of two numbers $b$ and $c$ is $a$,and $g_1$ and $g_2$ are two geometric means between them. If $g_1^3 + g_2^3 = kabc$,then $k = \dots$