Question

You bike 3 miles the first day of your​ training, 3.5 miles the second​ day, 4.5 miles the third​ day, and 6.5 miles the fourth day. If you continue this​ pattern, how many miles do you bike the seventh​ day?Question content area bottomPart 1On the seventh day you bikeenter your response here miles.

Answer 1

To find out how many miles you bike on the seventh day, let's first identify the pattern in the distances biked each day:

- Day 1: 3 miles
- Day 2: 3.5 miles
- Day 3: 4.5 miles
- Day 4: 6.5 miles

Now, let's look at the differences between the miles biked:

- Day 2 - Day 1: 3.5 - 3 = 0.5 miles
- Day 3 - Day 2: 4.5 - 3.5 = 1.0 miles
- Day 4 - Day 3: 6.5 - 4.5 = 2.0 miles

The differences between the daily distances are increasing as follows:
- From Day 1 to Day 2: increase of 0.5 miles
- From Day 2 to Day 3: increase of 1.0 miles
- From Day 3 to Day 4: increase of 2.0 miles

It appears that the differences in distance are doubling each day. To check how this continues, let's figure out the next increases:

- Increase from Day 4 to Day 5: (2.0 miles * 2) = 4.0 miles
- Increase from Day 5 to Day 6: (4.0 miles * 2) = 8.0 miles
- Increase from Day 6 to Day 7: (8.0 miles * 2) = 16.0 miles

Now, let's calculate the distances for days 5, 6, and 7:

- Day 5: 6.5 + 4.0 = 10.5 miles
- Day 6: 10.5 + 8.0 = 18.5 miles
- Day 7: 18.5 + 16.0 = 34.5 miles

Therefore, on the seventh day, you bike **34.5 miles**.