Question

100 POINTS FOR THE CORRECT ANSWER!!

Answer 1

14,11,8

Explanation:

If f(1)= 17

and f(n)= f(n-1) -3

f(2)= f(2-1)-3

f(2)=f(1)-3

f(2)=17-3

f(2)=14

f(3)=f(3-1)-3

f(3)=f(2)-3

f(3)=14-3

f(3)=11

f4)=f(4-1)-3

f(4)=f(3)-3

f(4)=11-3

f(4)=8

Answer 2

14, 11, 8

Explanation:

Given recursive formula:

`\begin{cases}f(1)=17\\f(n)=f(n-1)-3\end{cases}`

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:

`\begin{aligned}\implies f(2) & =f(2-1)-3\\& = f(1)-3\\& = 17-3\\& = 14\end{aligned}`

`\begin{aligned}\implies f(3) & =f(3-1)-3\\& = f(2)-3\\& = 14-3\\& = 11\end{aligned}`

`\begin{aligned}\implies f(4) & =f(4-1)-3\\& = f(3)-3\\& = 11-3\\& = 8\end{aligned}`