Using a geometric series, it is found that he swims 1897 yards in the first week.
In a geometric series, the quotient between consecutive terms is always the same, and it is called common ratio q.
The general equation of a geometric series is given by:
In which is the first term.
The sum of the first n terms is given by:
In this problem:
- 200 yards on the first day, thus
.
- Each day, the distance increases by 10%, since 100% + 10% = 110% = 1.1,
.
- First week is first 7 days, thus
Then:
He swims 1897 yards in the first week.
A similar problem is given at brainly.com/question/23711475