Read the story and respond to the requests below. Use the Format Editor x−−√ to type math or use the Image icon to upload a photo of your work.

Question

Kara is enrolled in a driver's training program. She drives 4 miles the first week of her training, 8 miles the second week, 16 miles the third week, and 32 miles the fourth week.

Write the sequence represented by the story.
Is the sequence arithmetic or geometric?
Does it have a common difference or common ratio?
What is the common difference or common ratio?
What are the next three terms?

Answer 1

The sequence of miles that Kara drives each week is as follows:

• Week 1: 4 miles
• Week 2: 8 miles
• Week 3: 16 miles
• Week 4: 32 miles

Sequence:

The sequence represented by the story is: \[ 4, 8, 16, 32 \]

Type of Sequence:

The sequence is geometric.

Common Difference or Ratio:

In a geometric sequence, we look for a common ratio rather than a common difference.

Common Ratio:

To find the common ratio, we can divide each term by the previous term:

• \( \frac{8}{4} = 2 \)
• \( \frac{16}{8} = 2 \)
• \( \frac{32}{16} = 2 \)

Thus, the common ratio is: \[ 2 \]

Next Three Terms:

To find the next three terms, we multiply the last term by the common ratio:

• 5th term: \( 32 \times 2 = 64 \)
• 6th term: \( 64 \times 2 = 128 \)
• 7th term: \( 128 \times 2 = 256 \)

Next Three Terms:

The next three terms are: \[ 64, 128, 256 \]

In summary:

• Sequence: \( 4, 8, 16, 32 \)
• Type: Geometric
• Common ratio: \( 2 \)
• Next three terms: \( 64, 128, 256 \)