Question

I NEED HELP ASAP!
A triathlete is preparing for a race. He swims 200 yards the first day of training. Each day after, he increases the number of yards he swims by 10% for 60 days.
The number of yards he swims can be represented in geometric series.
What is the total number of yards he swims in the first week? Round your answer to the nearest whole unit.

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 https://brainly.com/question/23711475