Question

after hip surgery, your physical therapist tells you to slowly return to walking. the therapist suggests walking for 5 minutes each day for the first week and increasing that time by 5 minutes per day each week thereafter. how many weeks will it be before you are up to 45 minutes of walking per day?
10
11
9
13

Explanation:

Step1: Identify the arithmetic sequence

The walking time per day forms an arithmetic sequence where the first term \(a_1 = 5\) (minutes per day in the first week), the common difference \(d = 5\) (minutes per day increase each week), and we want to find \(n\) when \(a_n=45\). The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\).

Step2: Substitute values into the formula

Substitute \(a_n = 45\), \(a_1=5\), and \(d = 5\) into the formula:
\[
45=5+(n - 1)\times5
\]

Step3: Solve for \(n\)

First, subtract 5 from both sides:
\[
45-5=(n - 1)\times5
\]
\[
40=(n - 1)\times5
\]
Then, divide both sides by 5:
\[
\frac{40}{5}=n - 1
\]
\[
8=n - 1
\]
Finally, add 1 to both sides:
\[
n=8 + 1=9
\]

Answer:

9