Answer:
[tex]a_n=200(0.6)^{n-1}[/tex]
Step-by-step explanation:
The explicit formula for a geometric sequence is [tex]a_n=a_1(r)^{n-1}[/tex] where [tex]a_n[/tex] is the [tex]n[/tex]th term, [tex]a_1[/tex] is the first term, and [tex]r[/tex] is the common ratio.
Here, the common ratio is [tex]r=0.6[/tex] because [tex]\frac{120}{200}=0.6[/tex], [tex]\frac{72}{120}=0.6[/tex], and so on. We also know that our first term is [tex]a_1=200[/tex], thus, our explicit formula for the geometric sequence is [tex]a_n=200(0.6)^{n-1}[/tex]
