# What is the 10th term of the geometric sequence 3, 9, 27,...?

Mar 18, 2018

${a}_{10} = 59049$

#### Explanation:

$\text{the nth term of a geometric sequence is}$

•color(white)(x)a_n=ar^(n-1)

$\text{where a is the first term and r the common ratio}$

$r = {a}_{2} / {a}_{1} = {a}_{3} / {a}_{2} = \ldots \ldots = {a}_{n} / {a}_{n - 1}$

$\text{here "a=3" and } r = \frac{9}{3} = \frac{27}{9} = 3$

$\Rightarrow {a}_{10} = 3 \times {3}^{9} = {3}^{10} = 59049$