The problem asks to find the first four terms of the sequence defined by the formula:

$a_n = 44 + (n - 1) \cdot 4, \quad n = 1, 2, 3, \ldots$

Let's calculate the first four terms by substituting $n = 1, 2, 3,$ and $4$ into the sequence formula:

1. For $n = 1$: $a_1 = 44 + (1 - 1) \cdot 4 = 44 + 0 = 44$

2. For $n = 2$: $a_2 = 44 + (2 - 1) \cdot 4 = 44 + 4 = 48$

3. For $n = 3$: $a_3 = 44 + (3 - 1) \cdot 4 = 44 + 8 = 52$

4. For $n = 4$: $a_4 = 44 + (4 - 1) \cdot 4 = 44 + 12 = 56$

Therefore, the first four terms of the sequence are:

$44, 48, 52, 56$

Would you like more details on how this sequence is generated, or do you have any specific questions?

Here are some related questions that might be useful for expanding your understanding:

1. How can we determine if a sequence is arithmetic or geometric?
2. What is the common difference in an arithmetic sequence?
3. How do we find the nth term of an arithmetic sequence?
4. How can sequences be used to solve real-world problems?
5. What is the sum of the first n terms of an arithmetic sequence?

Tip: For arithmetic sequences, the common difference can be identified by subtracting any term from the subsequent term, which remains constant throughout the sequence.