# What is the 9th term of the geometric sequence –1, 3, –9, …?

Jan 6, 2016

${a}_{9} = - 6561$

#### Explanation:

${a}_{2} / {a}_{1} = \frac{3}{-} 1 = - 3$

${a}_{3} / {a}_{2} = - \frac{9}{3} = - 3$

$\implies$ common ratio$= r = - 3$ and ${a}_{1} = - 1$

We know that:
${a}_{n} = {a}_{1} {r}^{n - 1}$
$\implies {a}_{9} = \left(- 1\right) {\left(- 3\right)}^{9 - 1} = \left(- 1\right) {\left(- 3\right)}^{8} = \left(- 1\right) 6561 = - 6561$
$\implies {a}_{9} = - 6561$