Question

A. What is the explicit definition for this sequence?b. How far does she run on day 19?​

Answer 1

Answer:

(a) $a_n=1+\frac{1}{6}(n-1)$

(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:

$a_n=a_1+(n-1)d\\a_n\to n^{th}\ term\\a_1\to first\ term\\n\to number\ of\ terms\\d\to \textrm{common difference}$

Here, $a_1=1,a_7=2$

So,

$a_7=a_1+(7-1)d\\2=1+6d\\6d=2-1\\d=\frac{1}{6}$

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

$a_n=1+\frac{1}{6}(n-1)$

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,

$a_{19}=1+\frac{1}{6}(19-1)\\\\a_{19}=1+\frac{1}{6}(18)\\\\a_{19}=1+3=4\ mi$

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