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
![S_{n} = \frac{n}{2}[2a_{1}+(n-1)d]](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B2a_%7B1%7D%2B%28n-1%29d%5D)
Where
is the nth term ,
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.

d = 0.25 miles
n = 12
Put all the values in the sum formula
![S_{12} = \frac{12}{2}[2\times 2+(12-1)0.25]](https://tex.z-dn.net/?f=S_%7B12%7D%20%3D%20%5Cfrac%7B12%7D%7B2%7D%5B2%5Ctimes%202%2B%2812-1%290.25%5D)
![S_{12} =6\times [4+11\times 0.25]](https://tex.z-dn.net/?f=S_%7B12%7D%20%3D6%5Ctimes%20%5B4%2B11%5Ctimes%200.25%5D)
![S_{12} =6\times [4+2.75]](https://tex.z-dn.net/?f=S_%7B12%7D%20%3D6%5Ctimes%20%5B4%2B2.75%5D)
![S_{12} =6\times [6.75]](https://tex.z-dn.net/?f=S_%7B12%7D%20%3D6%5Ctimes%20%5B6.75%5D)

Therefore the total number of miles Eli runs over the course of 12 days is 40.5 mi .