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.