To find the next three numbers in the sequence:

The sequence is: \(-5, -2, -3, 0, -1, 2, 1, 4\).

Let’s analyze the differences between consecutive numbers:

- From \(-5\) to \(-2\): \[ \text{Difference} = +3 \]
- From \(-2\) to \(-3\): \[ \text{Difference} = -1 \]
- From \(-3\) to \(0\): \[ \text{Difference} = +3 \]
- From \(0\) to \(-1\): \[ \text{Difference} = -1 \]
- From \(-1\) to \(2\): \[ \text{Difference} = +3 \]
- From \(2\) to \(1\): \[ \text{Difference} = -1 \]
- From \(1\) to \(4\): \[ \text{Difference} = +3 \]

The pattern alternates between \(+3\) and \(-1\).

Following this pattern:
- After \(4\), the difference will be \(-1\), so the next number is \(4 - 1 = 3\).
- After \(3\), the difference will be \(+3\), so the next number is \(3 + 3 = 6\).
- After \(6\), the difference will be \(-1\), so the next number is \(6 - 1 = 5\).

Thus, the next three numbers in the sequence are: **3, 6, 5**.

Would you like further clarification?

Here are some related questions:
1. Can you identify other types of alternating patterns in sequences?
2. How do arithmetic sequences differ from this alternating pattern?
3. What is a recursive formula for this sequence?
4. How could you model this pattern using a piecewise function?
5. How might this sequence behave if the differences were doubled?

**Tip**: When spotting patterns, always check for alternating sequences or a repeating cycle.

Discover the next three numbers in the sequence: -5, -2, -3, 0, -1, 2, 1, 4, by analyzing the alternating pattern of differences. This step-by-step guide is perfect for middle school students (Grades 6-8) learning to identify arithmetic patterns and sequences.

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