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The question is asking to identify the sequence that has a common ratio of \(-3\).

Let's analyze each option to determine the correct geometric sequence:

### 1. \(1, 3, 9, 27, 81\)
- The ratio between each term is \(\frac{3}{1} = 3\), \(\frac{9}{3} = 3\), etc. 
- The common ratio is \(3\), not \(-3\).

### 2. \(1, -3, 9, -27, 81\)
- The ratio between each term is \(\frac{-3}{1} = -3\), \(\frac{9}{-3} = -3\), \(\frac{-27}{9} = -3\).
- This has a common ratio of \(-3\), so **this is the correct sequence**.

### 3. \(9, 6, 3, 0, -3\)
- The ratio between the terms is not consistent. The difference between terms is \( -3 \) in some steps, but there is no constant ratio.
- This is an arithmetic sequence, not geometric.

### 4. \(9, 12, 15, 18, 21\)
- This is an arithmetic sequence with a common difference of \(3\), not a geometric sequence.

### Conclusion:
The correct sequence with a common ratio of \(-3\) is **option 2: \(1, -3, 9, -27, 81\)**.

Would you like further details or clarifications?

Here are 5 related questions for further practice:
1. What is the common ratio of the sequence \(2, -6, 18, -54\)?
2. How do you identify a geometric sequence from a list of numbers?
3. What is the sum of the first 5 terms of the sequence \(1, -3, 9, -27, 81\)?
4. How do geometric sequences differ from arithmetic sequences?
5. Can a geometric sequence have a ratio of \(0\)?

**Tip:** In a geometric sequence, the common ratio is found by dividing any term by the previous term.

Which sequence has a common ratio of (-3)?
1) 1, 3, 9, 27, 81
2) 1, -3, 9, -27, 81
3) 9, 6, 3, 0, -3
4) 9, 12, 15, 18, 21

In this problem, we explore how to identify a geometric sequence with a common ratio of -3. Learn the key concepts of geometric sequences and how to apply the common ratio formula to find the correct sequence. This problem is suitable for students in Grades 7-10.

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