Find three numbers in $\mathrm{G}.\mathrm{P}.$ whose product is $729$ and the sum of their products in pairs is $819$.

Find the sum of the following geometric progressions:

$2, \mathrm{6,} 18, ...$ to $7$ terms

Find the sum of the following geometric progression:

$1, 3, 9, 27, \dots$ to $8$ terms

Find the sum of the following geometric progressions:

$1, -\frac{1}{2}, \frac{1}{4}, -\frac{1}{8},........$ to $9$ term

Find the sum of the following geometric progressions:

$\left(a^2-b^2\right), \left(a-b\right), \left(\frac{a-b}{a+b}\right), ........$ to $n$ terms

Find the sum of the following geometric progressions:

$4 ,2, 1, \frac{1}{2}, ......$ to $10$ terms.

Find the sum of the following geometric series:

$0.15+0.015+0.0015+...$ to $8$ terms;

Find the sum of the following geometric series:

$\sqrt{2}+\frac{1}{\sqrt{2}}+\frac{1}{2\sqrt{2}}+\dots$ to $8$ terms;