https://file.aiquickdraw.com/mathbot/file/1729434073861bnf2ajdz.jpg

In this question, we are asked to identify which of the sequences is a geometric sequence. A **geometric sequence** is a sequence where each term after the first is obtained by multiplying the previous term by a constant, called the **common ratio**.

Let's analyze the given sequences:

- **A. 4, 2, 1, 1/2, 1/4,...**
  
  To check if it's geometric, we divide each term by the previous one:
  - \( \frac{2}{4} = 0.5 \)
  - \( \frac{1}{2} = 0.5 \)
  - \( \frac{1/2}{1} = 0.5 \)
  - \( \frac{1/4}{1/2} = 0.5 \)

  Since the ratio is consistent (0.5), **A** is a geometric sequence with a common ratio of 0.5.

- **B. 3, -15, -33, -51, -69,...**
  
  To check if this is geometric, we divide each term by the previous one:
  - \( \frac{-15}{3} = -5 \)
  - \( \frac{-33}{-15} \approx 2.2 \)
  - \( \frac{-51}{-33} \approx 1.55 \)

  The ratio is not constant, so **B** is not a geometric sequence.

- **C. 3, 6, 9, 12,...**
  
  This is an arithmetic sequence (each term is increased by 3), not geometric.

- **D. 2, 3, 5, 9, 17,...**
  
  There is no constant ratio between the terms, so **D** is not geometric.

### Correct Answer: **A**

Would you like more details or have any questions? Here are some additional questions for practice:

1. What is the formula for the nth term of a geometric sequence?
2. How do you find the sum of a geometric series?
3. Can a geometric sequence have negative terms?
4. How can you identify an arithmetic sequence versus a geometric sequence?
5. What is a real-world example of a geometric sequence?

**Tip**: In a geometric sequence, multiplying by a constant ratio every step is key. Always check the ratio between consecutive terms!

Learn how to identify a geometric sequence by examining common ratios in a sequence. This question helps students in Grades 6-8 understand key concepts in geometric progressions. Explore the correct and incorrect sequences with clear explanations.

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