If f, of, 1, equals, 2f(1)=2 and f, of, n, equals, f, of, n, minus, 1, minus, 4f(n)=f(n−1)−4 then find the value of f, of, 6f(6).

Let's analyze the function \( f(n) \) given by the recursive relation:

\[
f(1) = 2
\]

\[
f(n) = f(n-1) - 4 \quad \text{for } n > 1
\]

We need to find the value of \( f(6) \).

### Step 1: Calculate the first few terms using the recursive formula

- \( f(1) = 2 \)
- \( f(2) = f(1) - 4 = 2 - 4 = -2 \)
- \( f(3) = f(2) - 4 = -2 - 4 = -6 \)
- \( f(4) = f(3) - 4 = -6 - 4 = -10 \)
- \( f(5) = f(4) - 4 = -10 - 4 = -14 \)
- \( f(6) = f(5) - 4 = -14 - 4 = -18 \)

### Step 2: Conclusion
So, the value of \( f(6) \) is:

\[
\boxed{-18}
\]

Would you like more details on this solution or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would you find \( f(10) \) using the same recursive relation?
2. What is the general formula for \( f(n) \) based on this recursive definition?
3. Can you determine \( f(0) \) or \( f(-1) \) assuming the pattern continues?
4. What would happen if the recursive relation was \( f(n) = f(n-1) + 4 \)?
5. How would you verify if the function \( f(n) = -4n + 6 \) satisfies the given recursive relation?

**Tip:** Recursive functions often generate arithmetic sequences, where each term is a fixed step away from the previous one. Recognizing this pattern can help solve problems efficiently.

Learn how to find the value of f(6) using recursive functions with a detailed step-by-step solution. This problem covers recursive definitions, arithmetic sequences, and basic algebraic calculations. Suitable for students in Grades 7-9.

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