Question

I NEED HELP ASAP!

Answer 1

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:

$a_n = a_1q^{n-1}$

In which $a_1$ is the first term.

The sum of the first n terms is given by:

$S_{n} = \frac{a_1(1 - q^n)}{1 - q}$

In this problem:

• 200 yards on the first day, thus $a_1 = 200$.
• Each day, the distance increases by 10%, since 100% + 10% = 110% = 1.1, $q = 1.1$.
• First week is first 7 days, thus $n = 7$

Then:

$S_{n} = \frac{a_1(1 - q^n)}{1 - q}$

$S_{7} = \frac{200(1 - 1.1^7)}{1 - 1.1}$

$S_{7} = 1897$

He swims 1897 yards in the first week.

A similar problem is given at brainly.com/question/23711475