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 $f(n)$?

---

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.