Question
Which of these is a geometric sequence?
A. 2, 3, 5, 9, 17,…
В. 3, -15, -33, - 51, -69, ...
C. 3, 6, 9,12...
D. 4,2,1,1/2,1/4,…
A. 2, 3, 5, 9, 17,…
В. 3, -15, -33, - 51, -69, ...
C. 3, 6, 9,12...
D. 4,2,1,1/2,1/4,…
Answers
Answered by
GPT-4o mini
A geometric sequence is one in which each term after the first is found by multiplying the previous term by a constant factor (called the common ratio).
Let's analyze each option:
A. **2, 3, 5, 9, 17**: The differences between consecutive terms are not consistent - this is not a geometric sequence.
B. **3, -15, -33, -51, -69**: The ratios between consecutive terms are not consistent - this is not a geometric sequence.
C. **3, 6, 9, 12**: This is an arithmetic sequence (the common difference is 3), not a geometric sequence.
D. **4, 2, 1, 1/2, 1/4**: Here, each term is obtained by multiplying the previous term by a constant factor of 1/2.
Thus, the correct answer is **D. 4, 2, 1, 1/2, 1/4**, which is a geometric sequence with a common ratio of 1/2.
Let's analyze each option:
A. **2, 3, 5, 9, 17**: The differences between consecutive terms are not consistent - this is not a geometric sequence.
B. **3, -15, -33, -51, -69**: The ratios between consecutive terms are not consistent - this is not a geometric sequence.
C. **3, 6, 9, 12**: This is an arithmetic sequence (the common difference is 3), not a geometric sequence.
D. **4, 2, 1, 1/2, 1/4**: Here, each term is obtained by multiplying the previous term by a constant factor of 1/2.
Thus, the correct answer is **D. 4, 2, 1, 1/2, 1/4**, which is a geometric sequence with a common ratio of 1/2.
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