Question

Herman wants to build his endurance for running this year. The first week he runs 1.5 miles per day, the second week 2 miles per day. If this pattern continues, how many miles a day will he be running during the 10th week?

Answer 1

6 miles per day during the tenth week.

Explanation:

Given:

Miles per day in week 1 is,
`a_1=1.5`

Miles per day in week 2 is,
`a_2=2`

So, there is an increase of 2 - 1.5 = 0.5 miles from week 1 to week 2.

Therefore, the given pattern has a common difference of
`d= 0.5` and thus it follows an arithmetic sequence.

The
`n^(th)` term of an arithmetic sequence is given as:

`a_n=a_1+(n-1)d`

Here, 'n' represents the week and
`a_n` represents the miles per day in the week 'n'.

Now, we are asked to find the miles per day in week 10.

So,
`a_(10)=a_1+(10-1)d`

Plug in 0.5 for 'd' and
`a_1=1.5`. This gives,

`a_(10)=1.5+9* 0.5\\a_(10)=1.5+4.5\\a_(10)=6\ miles/day`

Therefore, Herman runs 6 miles per day during the tenth week.