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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

Find the first five terms of the given recursively defined sequence: a_n = 3(a_{n-1} - 3) with a_1 = 4.

Learn how to calculate the first five terms of the recursive sequence a_n = 3(a_{n-1} - 3) with a_1 = 4. This step-by-step guide covers recursive sequences and their calculations, suitable for students in Grades 9-12.

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