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The sequence is given as \([-1, 0, 1]\) repeated indefinitely. To solve this problem, let’s first analyze the sequence and determine the correctness of the given statements.

1. The sequence has a repeating cycle of 3 numbers: \([-1, 0, 1]\).
2. The position \(n\) in the sequence corresponds to the \( (n \mod 3) \) position in the cycle:
   - If \(n \mod 3 = 1\), the number is \(-1\).
   - If \(n \mod 3 = 2\), the number is \(0\).
   - If \(n \mod 3 = 0\), the number is \(1\).

### Checking each statement:

1. **11th number**:
   - \(11 \mod 3 = 2\), so the 11th number is \(0\).
   - **Incorrect** (not \(1\)).

2. **15th number**:
   - \(15 \mod 3 = 0\), so the 15th number is \(1\).
   - **Incorrect** (not \(0\)).

3. **16th number**:
   - \(16 \mod 3 = 1\), so the 16th number is \(-1\).
   - **Correct**.

4. **18th number**:
   - \(18 \mod 3 = 0\), so the 18th number is \(1\).
   - **Incorrect** (not \(-1\)).

### Conclusion:
The correct statement is **(3) 第16個數字是-1**.

Let me know if you’d like more details or further breakdown of the process!

### 5 Relative Questions:
1. How can modular arithmetic be used to solve problems with repeating sequences?
2. What are other examples of sequences with fixed patterns?
3. How do you determine the position in a repeating sequence efficiently?
4. Can you create a mathematical formula for the \(n\)th term in this type of sequence?
5. What are practical applications of modular arithmetic in real-world problems?

### Tip:
Modular arithmetic is a powerful tool for handling periodic patterns and simplifying computations in sequences.

小明將「-1, 0, 1」依序重複寫成數列「-1, 0, 1, -1, 0, 1, -1, 0, 1, …」。關於此數列，下列敘述何者正確？
(1) 第11個數字是1
(2) 第15個數字是0
(3) 第16個數字是-1
(4) 第18個數字是-1

Learn how to solve a repeating sequence problem involving modular arithmetic. The problem features a sequence that repeats as (-1, 0, 1), and the solution uses modular arithmetic to identify the correct terms. Suitable for Grades 7-9 students.

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