Mosquitoes are growing at a rate of $10\%$ a year. If there were $200$ mosquitoes in the beginning. Write down the number of mosquitoes after $n$ years.

If the sequence $3, 6, 12, 24,...$ is in G.P, find $S_n$.

If the sequence $p, q, \frac{q^2}{p}, \frac{q^3}{p},...$ is in G.P, find $S_n$.$$

If the sequence $0.7, 0.07, 0.007,...$ is in G.P, find $S_n$.

If the sequence $\sqrt{5}, -5, 5\sqrt{5}, -25,...$ is in G.P, find $S_n$.

For a G.P, if $a=2, r=-\frac{2}{3}$, then find $S_6$.