# How do you find the explicit formula for the following sequence 5, 0.5, 0.05, 0.005 ...?

Feb 5, 2016

$\left({x}_{n}\right) = 5 \cdot {\left(\frac{1}{10}\right)}^{n - 1}$ , $n \in \mathbb{N}$

#### Explanation:

This is a geometric sequence with common ratio $r = {x}_{n + 1} / {x}_{n} = \frac{1}{10}$.

The first term is $a = 5$.

Hence the general term is $\left({x}_{n}\right) = a {r}^{n - 1}$ , $n \in \mathbb{N}$.

$= 5 \cdot {\left(\frac{1}{10}\right)}^{n - 1}$