We are given a recursive function $f$ defined as follows:

• $f(1) = 2$
• $f(n) = f(n-1) - 3$ for $n > 1$

To find $f(5)$, we can apply the recursive relation step-by-step, starting from $f(1) = 2$.

Step-by-Step Calculation:

1. $f(2) = f(1) - 3 = 2 - 3 = -1$
2. $f(3) = f(2) - 3 = -1 - 3 = -4$
3. $f(4) = f(3) - 3 = -4 - 3 = -7$
4. $f(5) = f(4) - 3 = -7 - 3 = -10$

Thus, the value of $f(5)$ is:

$f(5) = -10$

Would you like to go into further details or have any questions?

Here are 5 related questions to expand on this:

1. What is the general formula for $f(n)$?
2. How do we prove that the given function is linear?
3. How does changing the recursive relation affect the function's values?
4. Can the recursive relation be solved for other types of sequences?
5. How would this recursive relation behave if the initial condition changed?

Tip: When working with recursive functions, it helps to calculate a few values manually to identify patterns or behaviors.