Answer:
14, 11, 8
Step-by-step explanation:
Given recursive formula:
[tex]\begin{cases}f(1)=17\\f(n)=f(n-1)-3\end{cases}[/tex]
A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence f(n) provided you know the value of the previous term in the sequence f(n-1).
Therefore, the next 3 terms in the sequence are:
[tex]\begin{aligned}\implies f(2) & =f(2-1)-3\\& = f(1)-3\\& = 17-3\\& = 14\end{aligned}[/tex]
[tex]\begin{aligned}\implies f(3) & =f(3-1)-3\\& = f(2)-3\\& = 14-3\\& = 11\end{aligned}[/tex]
[tex]\begin{aligned}\implies f(4) & =f(4-1)-3\\& = f(3)-3\\& = 11-3\\& = 8\end{aligned}[/tex]
