The given number pattern is $8, 5, 2$. To determine the 15th term, let's first identify the rule governing the pattern.

We can observe that each number is decreasing by 3:

• $8 - 3 = 5$
• $5 - 3 = 2$

This suggests that the pattern is an arithmetic sequence, where the common difference $d = -3$.

The general formula for the $n$-th term of an arithmetic sequence is:

$a_n = a_1 + (n - 1) \cdot d$

Where:

• $a_n$ is the $n$-th term,
• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the position of the term in the sequence.

Given:

• $a_1 = 8$,
• $d = -3$,
• $n = 15$.

Substitute these values into the formula:

$a_{15} = 8 + (15 - 1) \cdot (-3)$ $a_{15} = 8 + 14 \cdot (-3)$ $a_{15} = 8 - 42$ $a_{15} = -34$

Thus, the 15th term of the sequence is $\boxed{-34}$.

Would you like to go over the details of the calculation or explore similar sequences? Here are some related questions:

1. How can you determine if a sequence is arithmetic?
2. What would happen if the common difference was positive instead of negative?
3. How do you calculate the sum of the first $n$ terms of an arithmetic sequence?
4. Can this formula be used for other types of sequences, like geometric sequences?
5. What is the 20th term of the sequence?

Tip: When identifying an arithmetic sequence, always check the differences between consecutive terms to ensure they are constant!