Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = 2^{n}$.

Divide $155$ into three parts such that the three numbers are in a Geometric Progression $(GP)$ and the first term is $120$ less than the third term.

The sum of some terms of a $G.P.$ is $315$,whose first term and the common ratio are $5$ and $2$ respectively. Find the last term and the number of terms.

The greatest positive integer $k,$ for which $49^k+1$ is a factor of the sum $49^{125}+49^{124}+\ldots+49^{2}+49+1$ is

If $S$ is the sum to infinity of a $G.P.$,whose first term is $a$,then the sum of the first $n$ terms is

If the first term of an infinite geometric series is twice the sum of all its subsequent terms,what is the common ratio?