Question

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.

What is the total number of miles Eli runs over the course of 12 days?



39.5 mi

40.25 mi

40.5 mi

42.75 mi

Answer 1

He will run 40.5 miles in 12 days

Answer 2

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

Explanation:

The sum formula for airthmetic series is given by

`S_(n) = (n)/(2)[2a_(1)+(n-1)d]`

Where
`a_(n)` is the nth term ,
`a_(1)` 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.

`a_(1) =2`

d = 0.25 miles

n = 12

Put all the values in the sum formula

`S_(12) = (12)/(2)[2* 2+(12-1)0.25]`

`S_(12) =6* [4+11* 0.25]`

`S_(12) =6* [4+2.75]`

`S_(12) =6* [6.75]`

`S_(12) =40.5\ mi`

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