Answer:
[tex]a_n=\frac{2}{5} a_{n-1}[/tex]
[tex]a_1=500[/tex]
----------------------or one might prefer the answer so that [tex]r[/tex] is a decimal:
[tex]a_n=0.4 a_{n-1}[/tex]
[tex]a_1=500[/tex]
Step-by-step explanation:
The recursive form got a geometric sequence is [tex]a_n=r \cdot a_{n-1}[/tex] with a term given such as the first term, [tex]a_1[/tex].
[tex]r[/tex] can be determined by choosing a term from the sequence and dividing by it's previous term.
That is [tex]r=\frac{a_2}{a_1}[/tex] or [tex]\frac{a_3}{a_2}[/tex] or so on...
[tex]r=\frac{200}{500}=\frac{2}{5}[/tex]
So the recursive form for this sequence is:
[tex]a_n=\frac{2}{5} a_{n-1}[/tex]
[tex]a_1=500[/tex]
