Respuesta :
Answer:
Total number of miles Eli runs over the course of 12 days is 40.5 mi .
Step-by-step explanation:
The sum formula for airthmetic series is given by
[tex]S_{n} = \frac{n}{2}[2a_{1}+(n-1)d][/tex]
Where [tex]a_{n}[/tex] is the nth term , [tex]a_{1}[/tex] is the first term and d is the common difference .
As given
Eli runs 2 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.
[tex]a_{1} =2[/tex]
d = 0.25 miles
n = 12
Put all the values in the sum formula
[tex]S_{12} = \frac{12}{2}[2\times 2+(12-1)0.25][/tex]
[tex]S_{12} =6\times [4+11\times 0.25][/tex]
[tex]S_{12} =6\times [4+2.75][/tex]
[tex]S_{12} =6\times [6.75][/tex]
[tex]S_{12} =40.5\ mi[/tex]
Therefore the total number of miles Eli runs over the course of 12 days is 40.5 mi .
