You are given the function $f$, defined recursively as:

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

This recursive definition implies that each subsequent value of $f(n)$ is the previous value incremented by 1. We can deduce the values of $f(n)$ for some small $n$:

• $f(1) = 2$
• $f(2) = f(1) + 1 = 2 + 1 = 3$
• $f(3) = f(2) + 1 = 3 + 1 = 4$
• $f(4) = f(3) + 1 = 4 + 1 = 5$
• $f(5) = f(4) + 1 = 5 + 1 = 6$
• And so on...

General form:

This suggests that the function is increasing linearly. In fact, the recursive rule defines an arithmetic sequence. We can generalize it as:

$f(n) = f(1) + (n - 1)$

Since $f(1) = 2$, we have:

$f(n) = 2 + (n - 1) = n + 1$

Thus, the general formula for $f(n)$ is:

$f(n) = n + 1$

Would you like more details or further explanation?

Here are 5 related questions:

1. What is the value of $f(10)$?
2. How would the function change if $f(1)$ was a different value?
3. Can you derive the closed form of another recursive function?
4. What is the sum of $f(n)$ from $n = 1$ to $n = 5$?
5. How would the graph of $f(n) = n + 1$ look?

Tip: Recursive definitions are often simplified by recognizing patterns or converting them into a closed formula!