Question

What are the next two terms of the sequence: `4, -20, 100, -500`?

Answer 1

Is a geometric sequence of forst term `4` and ratio `-5`

Then the general term or generic term is `a_n=4(-5)^(n-1)`

Then `a_4=4(-5)^3=4·(-125)=-500`
`a_5=4·(-5)^4=2500`
`a_6=4(-5)^5=-12500`

Other waw to do it is:

Once known the ratio (-5), multiply the prior term by it
`(-500)·(-5)=2500`
`2500·(-5)=-12500`