Geometric Sequences

The numbers $4,12,36,108,\dots$ form a geometric progression. The common ratio $q$ equals:

In the geometric progression $(b_n{)}_{n\ge 1}$, $b_1=2$ and $q=3$. Determine $b_5$.

What is the sum of the infinite geometric series $1+\frac{1}{2}+\frac{1}{4}+\cdots$?

Compute ${\displaystyle \sum _{k=0}^5{2}^k}$.

A bank deposit of $\mathrm{\$}\mathrm{1,000}$ earns annual compound interest at $10\mathrm{\%}$. After $3$ years, the balance is closest to:

In a geometric progression with $b_1=5$ and $q=2$, the term $b_n=320$. Determine $n$.

Compute the sum $1+{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{8}}+\cdots$.

Compute the sum of the first $10$ terms of the geometric progression $1,2,4,8,\dots$.

The numbers $3$, $x$, $27$ are in geometric progression (with positive ratio). Determine $x$.

For the geometric progression $1,2,4,8,16,32,\dots$, the sum $b_2+b_4+b_6$ equals: