# Is the sequence 3, 12, 36, ... a geometric sequence?

Jul 2, 2015

Here, ${r}_{1} \ne {r}_{2}$, hence the sequence is not geometric.

#### Explanation:

The sequence given is $3 , 12 , 36$

In a geometric sequence, a constant common ratio $r$ is maintained all through out the sequence.

The common ratio, $r$ is obtained by dividing a term by its preceding term

Finding $r$

1) ${r}_{1} = \frac{12}{3} = 4$

2) ${r}_{2} = \frac{36}{12} = 3$

Since ${r}_{1} \ne {r}_{2}$ the sequence is not geometric.