You bike 1 mile the first day of your training, 1.3 miles the second day, 1.9 miles the third day, and 3.1 miles the fourth day. If you continue this pattern, how many miles do you bike the seventh day?
On the seventh day you bike miles.

19.9 miles

Step-by-step explanation:

In this problem we have:

is the distance travelled during the 1st day

is the distance travelled during the 2nd day

is the distance travelled during the 3rd day

is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

Which can be rewritten using the general formula:

This means that

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

So, the  distance travelled on the 7th day is 19.9 miles.