# How do you write the explicit formula for the following geometric sequence: -0.1, 0.03, -0.009, 0.0027, -0.00081, ...?

Sep 13, 2016

${n}^{t h}$ term of given geometric series is $\left(- 0.1\right) \times {\left(- 0.3\right)}^{n - 1}$

#### Explanation:

In the given geometric series

$\left\{- 0.1 , 0.03 , - 0.009 , 0.0027 , - 0.00081 , \ldots \ldots\right\}$,

the first term is $- 0.1$ and common ratio is $\frac{0.03}{- 0.1} = \frac{- 0.009}{0.03} = \frac{0.0027}{- 0.009} = \frac{- 0.00081}{0.0027} = - 0.3$

As the ${n}^{t h}$ term of a geometric series whose first term is $a$ and common ratio is $r$ is $a \times {r}^{n - 1}$

Hence ${n}^{t h}$ term of given geometric series is

$\left(- 0.1\right) \times {\left(- 0.3\right)}^{n - 1}$