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?

Answer 1

`S_(n) = ( a_(1(1- r^(n)) ) )/(1-r)`

Answer 2

Answer: Number of miles he runs for 12 days is 40.5 miles.

Explanation:

Since we have given that

Number of miles Eli run on his first day = 2 miles

Next day, he increases his distance run by 0.25 miles.

Number of miles Eli run on his second day = 2+0.25 = 2.25 miles

Number of miles Eli run on his third day = 2.25+0.25 = 2.5 miles

So, it becomes an arithmetic progression:

`2,2.25,2.5,....`

Number of days he runs for = 12 days

So, Total number of miles he runs over the course of 12 days is given by

`S_(12)=(12)/(2)(2a+(n-1)d)\\\\S_(12)=(12)/(2)(2* 2+(12-1)0.25)\\\\S_(12)=6(4+11* 0.25)\\\\S_(12)=6(6.75)\\\\S_(12)=40.5\ miles`

Hence, Number of miles he runs for 12 days is 40.5 miles.