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!