Write the first 6 terms of the
sequence defined by the
recursive rule below.

Question

Write the first 6 terms of the sequence defined by the recursive rule below. $$ f(1)=17, f(n)=f(n-1)-3 $$

UpStudy AI · Accepted Answer

1. The sequence is defined recursively by
   $$
   f(1)=17, \quad f(n)=f(n-1)-3 \quad \text{for } n \ge 2.
   $$

2. Compute the terms iteratively:
   - For $$ n=1 $$:  
     $$
     f(1)=17.
     $$
   - For $$ n=2 $$:  
     $$
     f(2)=f(1)-3=17-3=14.
     $$
   - For $$ n=3 $$:  
     $$
     f(3)=f(2)-3=14-3=11.
     $$
   - For $$ n=4 $$:  
     $$
     f(4)=f(3)-3=11-3=8.
     $$
   - For $$ n=5 $$:  
     $$
     f(5)=f(4)-3=8-3=5.
     $$
   - For $$ n=6 $$:  
     $$
     f(6)=f(5)-3=5-3=2.
     $$

3. The first 6 terms of the sequence are:
   $$
   17,\; 14,\; 11,\; 8,\; 5,\; 2.
   $$
The first 6 terms of the sequence are: 17, 14, 11, 8, 5, 2.

Write the first 6 terms of the
sequence defined by the
recursive rule below.

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