Question: Question 15 (Multiple Choice Worth 1 Points)\n(Simple Interest and Arithmetic Sequences MC)\n\nAfter hip surgery, your physical therapist tells you to slowly return to walking. The therapist suggests walking for 5 minutes each day\nfor 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?\n\n10\n11\n9\n13
1. **State the problem:** You start walking 5 minutes per day in the first week and increase the walking time by 5 minutes each week. We want to find how many weeks it takes to reach 45 minutes per day.\n\n2. **Identify the sequence type:** This is an arithmetic sequence where the first term $a_1 = 5$ minutes and the common difference $d = 5$ minutes.\n\n3. **Use the arithmetic sequence formula:** The $n$-th term of an arithmetic sequence is given by $$a_n = a_1 + (n-1)d.$$\n\n4. **Set up the equation to find $n$ when $a_n = 45$: $$45 = 5 + (n-1)5.$$**\n\n5. **Solve for $n$: $$45 = 5 + 5(n-1)$$\n$$45 = 5 + 5n - 5$$\n$$45 = 5n$$\n$$\cancel{5} \times 9 = \cancel{5} \times n$$\n$$n = 9.$$**\n\n6. **Interpretation:** It will take 9 weeks to reach 45 minutes of walking per day.\n\n**Final answer:** 9 weeks.