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Sagot :
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:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_{n} = \frac{a_1(1 - q^n)}{1 - q}[/tex]
In this problem:
- 200 yards on the first day, thus [tex]a_1 = 200[/tex].
- Each day, the distance increases by 10%, since 100% + 10% = 110% = 1.1, [tex]q = 1.1[/tex].
- First week is first 7 days, thus [tex]n = 7[/tex]
Then:
[tex]S_{n} = \frac{a_1(1 - q^n)}{1 - q}[/tex]
[tex]S_{7} = \frac{200(1 - 1.1^7)}{1 - 1.1}[/tex]
[tex]S_{7} = 1897[/tex]
He swims 1897 yards in the first week.
A similar problem is given at https://brainly.com/question/23711475
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