If f, of, 1, equals, 3f(1)=3 and f, of, n, equals, f, of, n, minus, 1, minus, 3f(n)=f(n−1)−3 then find the value of f, of, 4f(4).

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

1. \( f(1) = 3 \)
2. \( f(n) = f(n - 1) - 3 \) for \( n \geq 2 \)

We are tasked with finding the value of \( f(4) \).

### Step-by-step solution:

Using the recursive formula \( f(n) = f(n-1) - 3 \), we can calculate \( f(2) \), \( f(3) \), and \( f(4) \).

#### Step 1: Find \( f(2) \)
Using \( f(2) = f(1) - 3 \):
\[
f(2) = 3 - 3 = 0
\]

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

#### Step 3: Find \( f(4) \)
Using \( f(4) = f(3) - 3 \):
\[
f(4) = -3 - 3 = -6
\]

Thus, the value of \( f(4) \) is \( \boxed{-6} \).

Would you like a detailed explanation of any part of the solution? Here are five related questions to explore this concept further:

1. How can we generalize the recursive function for any \( n \)?
2. What is the pattern of the values for \( f(n) \) as \( n \) increases?
3. How would the function change if the recursive step was \( f(n) = f(n-1) - 2 \)?
4. What are the advantages of defining functions recursively versus explicitly?
5. Can we solve this problem using an explicit formula for \( f(n) \)?

**Tip:** In recursive sequences, it's useful to compute a few terms to identify any pattern before attempting a general solution.

If f(1) = 3 and f(n) = f(n-1) - 3, then find the value of f(4).

Learn how to solve a recursive function problem where f(1) = 3 and f(n) = f(n-1) - 3. This step-by-step solution helps you understand how to calculate f(4) using algebra and recursion. Suitable for students in Grades 6-8.

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