# Is the sequence geometric 2, 6, 18, 54,...?

Feb 11, 2016

Yes, the sequence is geometric

#### Explanation:

Let the series be ${x}_{1} , {x}_{2} , {x}_{3} , {x}_{4} , {x}_{5} , \ldots .$

If the ratios ${x}_{2} / {x}_{1} = {x}_{3} / {x}_{2} = {x}_{4} / {x}_{3} = {x}_{5} / {x}_{4} \ldots$ (Let this ratio be $r$)

then the sequence is called geometric.

Here $r$ is constantly $3$, Hence sequence is geometric