Question

Is the sequence geometric? if so, identify the common ratio 1/5,2/15,4/45,8/135,16/405,...

Answer 1

So have the sequence: $\frac{1}{5} , \frac{2}{15} , \frac{4}{45} , \frac{8}{135} , \frac{16}{145} ,...$
To check if the sequence is geometric, we are going to find its common ratio; to do it we are going to use the formula: $r= \frac{a_{n} }{a_{n-1}}$
where 
$r$ is the common ratio 
$a_{n}$ is the current term in the sequence 
$a_{n-1}$ is the previous term in the sequence
In other words we are going to divide the current term by the previous term a few times, and we will to check if that ratio is the same:

For $a_{n}= \frac{2}{15}$ and $a_{n-1}= \frac{1}{5}$:
$r= \frac{ \frac{2}{15} }{ \frac{1}{5} }$
$r= \frac{2}{3}$

For $a_{n}= \frac{4}{45}$ and $a_{n-1}= \frac{2}{15}$:
$r= \frac{ \frac{4}{45} }{ \frac{2}{15} }$
$r= \frac{2}{3}$

For $a_{n}= \frac{8}{135}$ and $a_{n-1}= \frac{4}{45}$:
$r= \frac{ \frac{8}{135} }{ \frac{4}{45} }$
$r= \frac{2}{3}$
As you can see, we have a common ratio!

We can conclude that our sequence is a geometric sequence and its common ratio is $\frac{2}{3}$ 

Answer 2

The answer is :

yes; $\frac{2}{3}$