Answer:
(a) [tex]a_n=1+\frac{1}{6}(n-1)[/tex]
(b) 4 miles
Step-by-step explanation:
Given:
The sequence of run is an arithmetic sequence.
Miles traveled on day 1 = 1 mile
Miles traveled on day 7 = 2 miles
(a).
Explicit formula for an arithmetic sequence is given as:
[tex]a_n=a_1+(n-1)d\\a_n\to n^{th}\ term\\a_1\to first\ term\\n\to number\ of\ terms\\d\to \textrm{common difference}[/tex]
Here, [tex]a_1=1,a_7=2[/tex]
So,
[tex]a_7=a_1+(7-1)d\\2=1+6d\\6d=2-1\\d=\frac{1}{6}[/tex]
Therefore, the explicit definition of the above sequence is given as:
[tex]a_n=1+\frac{1}{6}(n-1)[/tex]
Where, [tex]a_n[/tex] is the miles covered on [tex]n^{th}[/tex] day.
(b)
In order to find the distance covered by her on day 19, we plug in 19 for n in the above formula. This gives,
[tex]a_{19}=1+\frac{1}{6}(19-1)\\\\a_{19}=1+\frac{1}{6}(18)\\\\a_{19}=1+3=4\ mi[/tex]
Therefore, the number of miles covered by her on day 19 is 4 miles.
