Question

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?

Answer 1

69.75 miles

Step-by-step explanation:

Akim runs 1.75 miles on his first day of training.

He increases his distance run by 0.25 miles the day after that i.e.

He runs 1.75+0.25 miles

On third day again he increases his distance by 0.25 miles i.e.

He runs 1.75+0.25+0.25 miles

i.e. on nth day he runs 1.75+0.25(n-1)

Total number of miles Akim runs over the course of 18 days is:

`\Sigma_(n=1)^(18) 1.75+0.25(n-1)`

=69.75 miles

Answer 2

He runs 69.75 miles.

Step-by-step explanation:
This can be represented as an arithmetic sequence, since the same number of miles is added each day.

The explicit form for this arithmetic sequence would be 1.75+0.25(n-1). However, we also need the sum. Using technology,

`\Sigma_(n=1)^(18) 1.75+0.25(n-1)=69.75`.