Answer:
6 miles per day during the tenth week.
Step-by-step explanation:
Given:
Miles per day in week 1 is, [tex]a_1=1.5[/tex]
Miles per day in week 2 is, [tex]a_2=2[/tex]
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 [tex]d= 0.5[/tex] and thus it follows an arithmetic sequence.
The [tex]n^{th}[/tex] term of an arithmetic sequence is given as:
[tex]a_n=a_1+(n-1)d[/tex]
Here, 'n' represents the week and [tex]a_n[/tex] represents the miles per day in the week 'n'.
Now, we are asked to find the miles per day in week 10.
So, [tex]a_{10}=a_1+(10-1)d[/tex]
Plug in 0.5 for 'd' and [tex]a_1=1.5[/tex]. This gives,
[tex]a_{10}=1.5+9\times 0.5\\a_{10}=1.5+4.5\\a_{10}=6\ miles/day[/tex]
Therefore, Herman runs 6 miles per day during the tenth week.
