Find the geometric mean between: 3 and 12.

Find the geometric mean between: 256 and 64.

Find the geometric mean between: 25 and 625.

Find the geometric mean between: -4 and -25.

Find the geometric mean between: 8 and $\frac{32}{3}$.

Find the geometric mean between: $\frac{1}{64}$ and $\frac{1}{16}$.

Find the $\rm 2^{nd}$ term of a geometric sequence whose first and third terms are $\rm \frac{2}{3}$ and$\rm \frac{3}{2}$ respectively.

If the geometric mean between two numbers is 27 and the first number is 81, find the second number.

Two numbers are in the ratio of 2 : 1 and their geometric mean is 4. Find the numbers.

Two numbers are in the ratio of 8 : 3 and their geometric mean is $\rm\frac{1}{4}$, Find the numbers.

How many terms must be taken of the series 3+6+12+..., to make the sum 1533?