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

$f(1) = 5$

$f(n) = 5 \times f(n-1) \quad \text{for } n > 1$

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

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

• $f(1) = 5$
• $f(2) = 5 \times f(1) = 5 \times 5 = 25$
• $f(3) = 5 \times f(2) = 5 \times 25 = 125$
• $f(4) = 5 \times f(3) = 5 \times 125 = 625$
• $f(5) = 5 \times f(4) = 5 \times 625 = 3125$
• $f(6) = 5 \times f(5) = 5 \times 3125 = 15625$

Step 2: Conclusion

So, the value of $f(6)$ is:

$\boxed{15625}$

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 describe the general formula for $f(n)$ given this recursive definition?
2. What is $f(7)$ using the same pattern?
3. If the recursive relation was $f(n) = 3 \times f(n-1)$, what would $f(6)$ be?
4. Can you express $f(n)$ as a function of $n$ without using recursion?
5. What happens to $f(n)$ as $n$ becomes very large?

Tip: Recognizing that recursive functions like this can often be expressed as powers of a base can simplify finding large values.