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: \( 64, 128, 256 \)