Geometric Sequences practice questions — GCSE Maths

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

The numbers $a,b,c$ are in GP and $a+b+c=14$, $abc=64$. The middle term $b$ equals:

For the geometric progression $(b_n{)}_{n\ge 1}$ with $b_1=2$ and $q=\sqrt{5}$, compute $\lfloor b_4\rfloor$ (the integer part of $b_4$).

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

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

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

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

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:

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