Question

A. What is the explicit definition for this sequence?

b. How far does she run on day 19?​

Answer 1

(a)
`a_n=1+(1)/(6)(n-1)`

(b) 4 miles

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:

`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}`

Here,
`a_1=1,a_7=2`

So,

`a_7=a_1+(7-1)d\\2=1+6d\\6d=2-1\\d=(1)/(6)`

Therefore, the explicit definition of the above sequence is given as:

`a_n=1+(1)/(6)(n-1)`

Where,
`a_n` is the miles covered on
`n^(th)` 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,

`a_(19)=1+(1)/(6)(19-1)\\\\a_(19)=1+(1)/(6)(18)\\\\a_(19)=1+3=4\ mi`

Therefore, the number of miles covered by her on day 19 is 4 miles.