# Is the following a geometric sequence 3, 9, 27, 81,…?

Dec 14, 2015

Yes. It is a geometric sequence with initial term ${a}_{0} = 3$ and common ratio $r = 3$.

#### Explanation:

A geometric sequence is a sequence of the form

${a}_{0} , {a}_{0} r , {a}_{0} {r}^{2} , {a}_{0} {r}^{3} , \ldots , {a}_{0} {r}^{n} , \ldots$

where ${a}_{0}$ is the first term in the sequence and $r$ is the common ratio between terms.

Looking at the given sequence, we can write it as

$3 , 3 \cdot {3}^{1} , 3 \cdot {3}^{2} , 3 \cdot {3}^{3} , \ldots$

which matches the pattern for the first term ${a}_{0} = 3$ and common ratio $r = 3$.