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.