The sum of the series $5.05 + 1.212 + 0.29088 + \dots \infty$ is

The sum of the first three terms of a $G.P.$ is $\frac{13}{12}$ and their product is $-1$. Find the common ratio and the terms.

Which term of the following sequence: $2, 2\sqrt{2}, 4, \ldots$ is $128$ (in $^{\text{th}}$)?

If the $4^{th}$,$7^{th}$,and $10^{th}$ terms of a Geometric Progression $(GP)$ are $a, b,$ and $c$ respectively,then:

If in an infinite $G.P.$ the first term is equal to twice the sum of the remaining terms,then its common ratio is

$A$ person has $2$ parents,$4$ grandparents,$8$ great-grandparents,and so on. Find the total number of his ancestors during the $10$ generations preceding his own.