First, we are going to simplify the fractions into ratios using this formula:
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
So...
[tex]\frac{-100}{500}=-\frac{1}{5},\:\quad \frac{20}{-100}=-\frac{1}{5},\:\quad \frac{-4}{20}=-\frac{1}{5}[/tex]
The sequence is geometric. Since we have to multiply the number by [tex]- \frac{1}{5} [/tex] to get the next number.
If the first element of the sequence is 500, the next one is calculated by:
[tex]n=500\left(-\frac{1}{5}\right)[/tex]
Have nice day! :)
