Given the function $f(n)$ defined recursively as:

$f(0) = -23$ $f(n) = f(n-1) + 4 \quad \text{for } n > 0$

This means that each subsequent value of $f(n)$ is obtained by adding 4 to the previous value of the function.

Let's calculate the first few values of $f(n)$:

• $f(0) = -23$
• $f(1) = f(0) + 4 = -23 + 4 = -19$
• $f(2) = f(1) + 4 = -19 + 4 = -15$
• $f(3) = f(2) + 4 = -15 + 4 = -11$
• $f(4) = f(3) + 4 = -11 + 4 = -7$

General formula:

We can also express $f(n)$ using a formula: $f(n) = f(0) + 4n$

Substituting $f(0) = -23$: $f(n) = -23 + 4n$

This is the explicit formula for $f(n)$.

Would you like more details on this or have any questions?

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Here are some related questions:

1. What would $f(10)$ be using the general formula?
2. How would the function change if the initial value was different?
3. How can you determine the value of $n$ when $f(n) = 0$?
4. How would the recursion change if the increment was a different value, say 5?
5. What is the significance of the recursive definition in general problem solving?

Tip: Understanding recursive functions helps in tackling complex problems by breaking them into simpler, repetitive steps.