Determine the Next Number in the Arithmetic Sequence: -6, -3, 0, 3, 6, ?

To solve this problem, we will examine the differences between consecutive terms in the given sequence:
The sequence is $-6, -3, 0, 3, 6$.

• Step 1: Find the difference between consecutive terms.
  • From $-6$ to $-3$: $-3 - (-6) = 3$
  • From $-3$ to $0$: $0 - (-3) = 3$
  • From $0$ to $3$: $3 - 0 = 3$
  • From $3$ to $6$: $6 - 3 = 3$
• Step 2: Verify that the difference is consistent. The common difference $d$ is $3$.
• Step 3: Use the common difference to find the next term in the sequence:
  From $6$, add the common difference ($3$): $6 + 3 = 9$.

Therefore, the next number in the sequence is $9$.

This matches choice 3 in the provided answer choices.