First, we are going to find the common ratio of our geometric sequence using the formula: [tex]r= \frac{a_{n}}{a_{n-1}} [/tex]. For our sequence, we can infer that [tex]a_{n}=-20[/tex] and [tex]a_{n-1}=4[/tex]. So lets replace those values in our formula:
[tex]r= \frac{-20}{4} [/tex]
[tex]r=-5[/tex]
Now that we have the common ratio, lets find the explicit formula of our sequence. To do that we are going to use the formula: [tex]a_{n}=a_{1}*r^{n-1}[/tex]. We know that [tex]a_{1}=4[/tex]; we also know for our previous calculation that [tex]r=-5[/tex]. So lets replace those values in our formula:
[tex]a_{n}=4*(-5)^{n-1}[/tex]
Finally, to find the 9th therm in our sequence, we just need to replace [tex]n[/tex] with 9 in our explicit formula:
[tex]a_{9}=4*(-5)^{9-1}[/tex]
[tex]a_{9}=4*(-5)^{8}[/tex]
[tex]a_{9}=1562500[/tex]
We can conclude that the 9th term in our geometric sequence is 1,562,500
