PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Akim runs 1.75 miles on his first day of training for a road race. The next day, he increases his distance run by 0.25 miles. The day after that, he increases his distance run by another 0.25 miles, and so on.

What is the total number of miles Akim runs over the course of 18 days?

Question

contestada

Respuesta :

tramserran tramserran · Answer 1 · 2019-01-23T09:42:13+01:00

Answer: 69.75 miles

Step-by-step explanation:

The explicit rule for an arithmetic sequence is: [tex]a_n=a_1+d(n-1)\ \text{where}\ a_1\ \text{is the first term and d is the difference}[/tex]

In the given problem, [tex]a_1=1.75[/tex] and d = 0.25

[tex]a_n=1.75+0.25(n-1)\\.\quad=1.75+0.25n-0.25\\.\quad=0.25n+1.50\\\\a_{18}=0.25(18)+1.50\\.\quad=4.50+1.50\\.\quad=6.00[/tex]

The sum of an arithmetic sequence is: [tex]S_n=\dfrac{a_1+a_n}{2}\cdot n[/tex]

[tex]S_{18}=\dfrac{1.75+6}{2}\cdot 18\\\\.\quad=7.75\cdot 9\\\\.\quad=69.75[/tex]

raphealnwobi raphealnwobi · Answer 2 · 2022-04-12T10:45:14+02:00

The total number of miles Akim runs over the course of 18 days is 69.75 miles

An arithmetic sequence has a first term (a) and the common difference.

This problem can be represented by an arithmetic sequence, with first term a = 1.75;

common difference (d) = 0.25

The total number of miles Akim runs over the course of 18 days

[tex]S_{18}=\frac{n}{2}(2a+(n-1)d)=\frac{18}{2}(2(1.75)+(18-1)0.25)= 69.75[/tex]

The total number of miles Akim runs over the course of 18 days is 69.75 miles

Find out more on arithmetic sequence at: https://brainly.com/question/6561461