The problem you're working with involves a recurrence relation where:

$a_1 = 0, \quad a_2 = 1, \quad a_n = a_{n-1} + a_{n-2}$

This is the Fibonacci sequence. Let's calculate the next terms:

Step-by-step:

• $a_3 = a_2 + a_1 = 1 + 0 = 1$
• $a_4 = a_3 + a_2 = 1 + 1 = 2$
• $a_5 = a_4 + a_3 = 2 + 1 = 3$

Thus, the values are:

• $a_3 = 1$
• $a_4 = 2$
• $a_5 = 3$

Do you want any further explanation or details about this solution?

Here are five related questions to expand on this:

1. What is the general form of a Fibonacci sequence?
2. Can you derive a closed-form expression for $a_n$ in the Fibonacci sequence?
3. What are the properties of the Fibonacci sequence in relation to the golden ratio?
4. How does the Fibonacci sequence appear in nature or geometry?
5. Can you solve a similar recurrence relation with different initial conditions?

Tip: The Fibonacci sequence grows exponentially, and its growth rate is closely related to the golden ratio $\phi$.