Final answer:
Option D (1/4, 1/2, 1, 2, 4) is the geometric sequence as there is a consistent common ratio of 2 between consecutive terms.
Step-by-step explanation:
To identify which of the given sequences is a geometric sequence, we need to look for a consistent ratio between consecutive terms. Here's how we examine each option:
- A. 3, -15, -33, -51, -69, ... does not have a common ratio. The differences are not consistent, and it's not multiplying by a common factor.
- B. 2, 3, 5, 9, 17, ... also does not have a common ratio; these numbers do not fit the pattern of a geometric sequence as they are not formed by multiplying the previous term by a fixed number.
- C. 1, 5, 9, 13, ... is an arithmetic sequence, not a geometric one, since each term is obtained by adding a common difference.
- D. 1/4, 1/2, 1, 2, 4 is a geometric sequence. Each term is obtained by multiplying the previous term by the common ratio of 2.
Therefore, the correct answer is D. 1/4, 1/2, 1, 2, 4, which clearly shows a common ratio of 2 between each term in the sequence.