Final answer:
Saac's car's fuel efficiency indicates an arithmetic sequence with a slight increase in miles per gallon each week, by approximately half a mile per gallon.
Step-by-step explanation:
The student has provided data points representing the miles per gallon (mpg) his car gets per week: (1, 24), (2, 24.48), (3, 24.97), and (4, 25.47). The task is to determine whether these data points have a common difference (indicating an arithmetic sequence) or a common ratio (indicating a geometric sequence).
To determine the common difference, we subtract each mpg value from the subsequent week's value:
- Week 2 - Week 1: 24.48 - 24 = 0.48
- Week 3 - Week 2: 24.97 - 24.48 = 0.49
- Week 4 - Week 3: 25.47 - 24.97 = 0.50
As per the above calculations, the differences between consecutive weeks' mpg are not exactly the same but are quite close, suggesting that Saac's car's fuel efficiency increases by approximately half a mile per gallon each week. This pattern is consistent with an arithmetic sequence.
Let's also check the ratio, even though we've identified an arithmetic sequence, to ensure it's not geometric.
- Week 2 / Week 1: 24.48 / 24 ≈ 1.02
- Week 3 / Week 2: 24.97 / 24.48 ≈ 1.02
- Week 4 / Week 3: 25.47 / 24.97 ≈ 1.02
The ratios are approximately the same but still not exact, further confirming we are looking at an arithmetic sequence with a small, increasing common difference rather than a constant geometric ratio.