The function \( f(n) \) is defined as follows:

1. \( f(1) = 5 \)
2. For \( n > 2 \), \( f(n) = \frac{1}{2} \times f(n-1) \)

This appears to be a recursive function, where each term is half of the previous term.

Let's compute the values for the first few terms to better understand the pattern:

- \( f(1) = 5 \)
- \( f(2) = \frac{1}{2} \times f(1) = \frac{1}{2} \times 5 = 2.5 \)
- \( f(3) = \frac{1}{2} \times f(2) = \frac{1}{2} \times 2.5 = 1.25 \)
- \( f(4) = \frac{1}{2} \times f(3) = \frac{1}{2} \times 1.25 = 0.625 \)
- And so on.

It looks like \( f(n) \) follows a geometric progression with the common ratio \( \frac{1}{2} \), and the first term \( f(1) = 5 \).

Would you like me to calculate more terms or derive a closed-form formula for \( f(n) \)?

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Here are some relative questions to expand on this topic:

1. How do you find a closed-form expression for a recursive sequence?
2. What is the general form of a geometric sequence, and how does it apply here?
3. How would you modify this sequence if the common ratio was a different value?
4. What happens to \( f(n) \) as \( n \to \infty \)?
5. How do recursive functions like this one compare to explicit functions in terms of ease of calculation?

**Tip**: Recursive functions are useful when breaking down problems into smaller, simpler sub-problems.

Explore the recursive function f(n) = (1/2) * f(n-1) with initial value f(1) = 5. Learn how to compute terms of this geometric sequence and derive a closed-form expression. Suitable for high school students in Grades 9-12.

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