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.