a.
In order to find the common ratio, we just need to divide a term by the term that comes before it.
So using the terms 20 and -5, we have:
[tex]\text{ratio}=\frac{20}{-5}=-4[/tex]b.
The recursive rule can be found with the formula:
[tex]a_n=a_{n-1}\cdot q[/tex]Where an is the nth term and q is the ratio. So we have:
[tex]a_n=a_{n-1}\cdot(-4)[/tex]c.
The explicit rule can be written as:
[tex]a_n=a_1\cdot q^{n-1}[/tex]Where an is the nth term, a1 is the first term and q is the ratio. So:
[tex]a_n=-5\cdot(-4)^{n-1}[/tex]