Answer:
[tex]T_{n}[/tex] = [tex]\frac{1}{5}[/tex] [tex]T_{n-1}[/tex] with T₁ = 5000
Step-by-step explanation:
There is a common ratio r between consecutive terms in the sequence, that is
r = [tex]\frac{1000}{5000}[/tex] = [tex]\frac{200}{1000}[/tex] = [tex]\frac{40}{200}[/tex] = [tex]\frac{1}{5}[/tex]
This indicates the sequence is geometric with recursive rule
[tex]T_{n}[/tex] = r [tex]T_{n-1}[/tex]
Here tr = [tex]\frac{1}{5}[/tex] , thus
[tex]T_{n}[/tex] = [tex]\frac{1}{5}[/tex] [tex]T_{n-1}[/tex] , T₁ = 5000
