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

So have the sequence: [tex] \frac{1}{5} , \frac{2}{15} , \frac{4}{45} , \frac{8}{135} , \frac{16}{145} ,...[/tex]
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: [tex]r= \frac{a_{n} }{a_{n-1}} [/tex]
where 
[tex]r[/tex] is the common ratio 
[tex]a_{n}[/tex] is the current term in the sequence 
[tex]a_{n-1}[/tex] 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 [tex]a_{n}= \frac{2}{15} [/tex] and [tex]a_{n-1}= \frac{1}{5} [/tex]:
[tex]r= \frac{ \frac{2}{15} }{ \frac{1}{5} } [/tex]
[tex]r= \frac{2}{3} [/tex]

For [tex]a_{n}= \frac{4}{45} [/tex] and [tex]a_{n-1}= \frac{2}{15} [/tex]:
[tex]r= \frac{ \frac{4}{45} }{ \frac{2}{15} } [/tex]
[tex]r= \frac{2}{3} [/tex]

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

We can conclude that our sequence is a geometric sequence and its common ratio is [tex] \frac{2}{3} [/tex]