Answer:
625
Explanation:
So this says the following:
A term is equal to 5 times the previous term.
We are given the 0th- term is 5.
The first term is 5(5)=25.
The second term would be 5(25)=125.
The third term would be 5(125)=625.
So f(3)=625.
If you didn't like that explanation, you can find f(3), by first finding f(1) then f(2) using the equation given as is without making the interpretation I did above.
[tex]f(n)=5 \cdot f(n-1)[/tex] ; plug in 1 for [tex]n[/tex]:
[tex]f(1)=5 \cdot f(1-1)[/tex]
[tex]f(1)=5 \cdot f(0)[/tex]
[tex]f(1)=5 \cdot 5[/tex]
[tex]f(1)=25[/tex]
[tex]f(n)=5 \cdot f(n-1)[/tex] ; plug in 2 for [tex]n[/tex]:
[tex]f(2)=5 \cdot f(2-1)[/tex]
[tex]f(2)=5 \cdot f(1)[/tex]
[tex]f(2)=5 \cdot 25[/tex]
[tex]f(2)=125[/tex]
[tex]f(n)=5 \cdot f(n-1)[/tex] ; plug in 3 for [tex]n[/tex]:
[tex]f(3)=5 \cdot f(3-1)[/tex]
[tex]f(3)=5 \cdot f(2)[/tex]
[tex]f(3)=5 \cdot 125[/tex]
[tex]f(3)=625[/tex]
