Question

which answer represents a geometric sequence?
{17,10,3, - 4,...}
{0,2,4,8,...}
{5,10,15,20,...}
{1,3,9,27,...}

Explanation:

Step1: Recall geometric - sequence definition

A geometric sequence has a common ratio $r$, where $r=\frac{a_{n + 1}}{a_{n}}$ for $n\geq1$.

Step2: Check the first sequence $\{17,10,3, - 4,\cdots\}$

$r_1=\frac{10}{17}
eq\frac{3}{10}$, so it's not a geometric sequence.

Step3: Check the second sequence $\{0,2,4,8,\cdots\}$

Since the first - term is $0$, and $\frac{2}{0}$ is undefined, it's not a geometric sequence.

Step4: Check the third sequence $\{5,10,15,20,\cdots\}$

$r_3=\frac{10}{5} = 2$, $\frac{15}{10}=\frac{3}{2}$, $2
eq\frac{3}{2}$, so it's not a geometric sequence.

Step5: Check the fourth sequence $\{1,3,9,27,\cdots\}$

$r_4=\frac{3}{1}=3$, $\frac{9}{3}=3$, $\frac{27}{9}=3$. It has a common ratio of $3$.

Answer:

{1,3,9,27,...}