Question

On her cell phone plan, Tina used 6 minutes in June, 30 minutes in July, 150 minutes in August, and 750 minutes in September. What kind of sequence is this?

Answer 1

To determine the type of sequence represented by the minutes Tina used in her cell phone plan, we can list the values she used for each month: 6 minutes in June, 30 minutes in July, 150 minutes in August, and 750 minutes in September.

Let’s write these values out:
- June: 6
- July: 30
- August: 150
- September: 750

Now, let's analyze the ratios between consecutive terms to check if it forms a geometric progression:

1. From June to July:
\[
\frac{30}{6} = 5
\]

2. From July to August:
\[
\frac{150}{30} = 5
\]

3. From August to September:
\[
\frac{750}{150} = 5
\]

Since the ratio between each pair of consecutive terms is constant \( (5) \), this indicates that the sequence is a geometric sequence with a common ratio of 5.

Therefore, the type of sequence that Tina's cell phone minute usage follows is a **geometric sequence**.