If f, of, 1, equals, 6*f*(1)=6 and f, of, n, equals, f, of, n, minus, 1, minus, 3*f*(*n*)=*f*(*n*−1)−3 then find the value of f, of, 5*f*(5).

We are given the function \( f(n) \) defined as follows:

\[
f(1) = 6
\]

\[
f(n) = f(n-1) - 3 \text{ for } n > 1
\]

We need to find the value of \( f(5) \).

### Step 1: Calculate \( f(2) \)
\[
f(2) = f(1) - 3 = 6 - 3 = 3
\]

### Step 2: Calculate \( f(3) \)
\[
f(3) = f(2) - 3 = 3 - 3 = 0
\]

### Step 3: Calculate \( f(4) \)
\[
f(4) = f(3) - 3 = 0 - 3 = -3
\]

### Step 4: Calculate \( f(5) \)
\[
f(5) = f(4) - 3 = -3 - 3 = -6
\]

Thus, the value of \( f(5) \) is \( \boxed{-6} \).

Would you like more details or have any questions? Here are 5 related questions to consider:
1. What would be the value of \( f(6) \)?
2. How can you generalize the function \( f(n) \) for any \( n \)?
3. How would the function change if \( f(n) = f(n-1) - k \) where \( k \) is a constant?
4. What if \( f(1) \) was a different value? How would that affect \( f(5) \)?
5. Can you derive a direct formula for \( f(n) \) without calculating step by step?

**Tip:** For functions defined recursively, try to identify a pattern or relation to simplify calculations for larger \( n \).

If f(1) = 6 and f(n) = f(n-1) - 3, then find the value of f(5).

Learn how to solve a recursive function problem where f(1) = 6 and f(n) = f(n-1) - 3. This step-by-step solution will guide you through finding the value of f(5), making it suitable for students in Grades 6-8.

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