Question

A woman decides to begin a routine exercise regimen. She begins walking 5 kilometers per week and adds 3 kilometers each week for 13 more weeks. How many kilometers did she walk in the 14 th week?

Answer 1

The woman increased her walking distance by 3 kilometers each week, starting at 5 kilometers in the first week. Using an arithmetic sequence formula, she walked 44 kilometers in the 14th week.

Step-by-step explanation:

The student's question relates to a mathematical sequence where the woman increases the distance she walks each week by a constant amount. To find out how many kilometers she walked in the 14th week, we need to consider this increase as part of an arithmetic sequence. The sequence begins with 5 kilometers in the first week and increases by 3 kilometers each week.

To calculate the distance walked in the 14th week, we use the formula for the n-th term of an arithmetic sequence, which is an = a1 + (n - 1) * d, where an is the distance in the n-th week, a1 is the initial distance, n is the week number, and d is the common difference between terms (in this case, the weekly increase).

Using the formula:

a1 = 5 km (initial distance)d = 3 km (weekly increase)n = 14 (week number)

We can calculate the distance for the 14th week as follows:

a14 = 5 km + (14 - 1) * 3 km
= 5 km + 13 * 3 km
= 5 km + 39 km
= 44 km

Therefore, the woman walked 44 kilometers in the 14th week of her exercise regimen.