Question
Which of these is a geometric sequence?
1,5,9,13…
3,-15,-33,-51,-69…
2,3,5,9,17…
1,5,9,13…
3,-15,-33,-51,-69…
2,3,5,9,17…
Answers
GPT-4o mini
A geometric sequence is defined as a sequence where each term after the first is found by multiplying the previous term by a constant factor (common ratio).
Let's analyze the sequences you provided:
1. **1, 5, 9, 13...**: This sequence is an arithmetic sequence (each term increases by 4), not a geometric sequence.
2. **3, -15, -33, -51, -69...**: This sequence does not have a constant ratio between terms. For example, -15 / 3 = -5, but -33 / -15 = 2.2, and so on. Therefore, it's not a geometric sequence.
3. **2, 3, 5, 9, 17...**: This sequence also does not have a constant ratio. The ratios between the terms are as follows: 3/2 (1.5), 5/3 (1.67), and so on, which are not equal. Thus, this is not a geometric sequence.
None of the sequences you provided are geometric sequences.
Let's analyze the sequences you provided:
1. **1, 5, 9, 13...**: This sequence is an arithmetic sequence (each term increases by 4), not a geometric sequence.
2. **3, -15, -33, -51, -69...**: This sequence does not have a constant ratio between terms. For example, -15 / 3 = -5, but -33 / -15 = 2.2, and so on. Therefore, it's not a geometric sequence.
3. **2, 3, 5, 9, 17...**: This sequence also does not have a constant ratio. The ratios between the terms are as follows: 3/2 (1.5), 5/3 (1.67), and so on, which are not equal. Thus, this is not a geometric sequence.
None of the sequences you provided are geometric sequences.