# What is the 9th term of the geometric sequence 3, 9, 27,...?

Mar 4, 2018

I get $19683$.

#### Explanation:

The sequence is:

$3 , 9 , 27 , \ldots$

or we can write it as

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

So, the pattern is just powers of $3$.

I see immediately that if $n$ is the term in the sequence, it is given by ${3}^{n} , n \in \mathbb{N}$.

So, the sequence is

${a}_{n} = {3}^{n}$, where ${a}_{n}$ is the ${n}^{\text{th}}$ term.

Therefore, the ninth term will be

${a}_{9} = {3}^{9}$

$= 19683$