The problem asks to find the first five terms of the recursively defined sequence, where the sequence is defined by:

$a_n = 3(a_{n-1} - 3) \quad \text{with} \quad a_1 = 4$

We will calculate the first five terms step by step using the recursive formula.

Step-by-step calculations:

1. $a_1 = 4$ (Given)
2. $a_2 = 3(a_1 - 3) = 3(4 - 3) = 3(1) = 3$
3. $a_3 = 3(a_2 - 3) = 3(3 - 3) = 3(0) = 0$
4. $a_4 = 3(a_3 - 3) = 3(0 - 3) = 3(-3) = -9$
5. $a_5 = 3(a_4 - 3) = 3(-9 - 3) = 3(-12) = -36$

The first five terms of the sequence are:

$a_1 = 4, \quad a_2 = 3, \quad a_3 = 0, \quad a_4 = -9, \quad a_5 = -36$

Would you like more details on the recursive process or further clarification?

Here are 5 related questions to expand on this concept:

1. What would the next term $a_6$ be in this sequence?
2. How does this recursive relation behave as $n$ increases? Does the sequence converge?
3. Can you derive a general formula for