Final answer:
A geometric sequence is characterized by a constant ratio between consecutive terms. To determine if a sequence is geometric, you calculate the ratio between terms and check its consistency.
Step-by-step explanation:
The information provided does not explicitly state any geometric sequences, but I can explain how to identify a geometric sequence and give an example.
A geometric sequence is a sequence where each term after the first is found by multiplying the previous term by a constant called the common ratio (r).
Steps to Identify a Geometric Sequence:
- Calculate the ratio between consecutive terms.
- Check if this ratio is consistent throughout the sequence.
For example, the sequence 3, 6, 12, 24, ... is geometric because each term is multiplied by the common ratio 2 to get the next term (6 ÷ 3 = 2, 12 ÷ 6 = 2, and so on).
If you're using a TI-83+, TI-83, or TI-84 calculator, to identify if a sequence is geometric, you would:
- Enter the sequence into a list.
- Use the 'Seq' function to generate terms based on a formula.
- Analyze the ratio of consecutive terms using the ratio test.
In summary, for a sequence to be geometric, it must have a constant ratio when any term is divided by its preceding term.