If the half-life period of a substance is $5$ years,then the total amount of the substance left after $15$ years,when the initial amount is $64$ gms,is: (in $gms$)

If the $(p + q)^{th}$ term of a geometric progression is $m$ and the $(p - q)^{th}$ term is $n$,then what is the $p^{th}$ term?

The sum of an infinite geometric series with positive terms is $3$ and the sum of the cubes of its terms is $\frac{27}{19}$. Then the common ratio of this series is

If $G_1$ and $G_2$ are two geometric means between two numbers and $A$ is the arithmetic mean between them,then find the value of $\frac{G_1^2}{G_2} + \frac{G_2^2}{G_1}$.

Consider a geometric progression with first term $a$ and common ratio $r$. If $A$ and $H$ are the arithmetic mean and harmonic mean of the first $n$ terms of the geometric progression respectively,then $A \cdot H = \dots$

Suppose the sides of a triangle form a geometric progression with common ratio $r$. Then,$r$ lies in the interval