Question

Abby has just started training for a marathon. She ran 15 miles in total during her first week of training. She wants to add an additional 2 miles to her weekly total during each subsequent week. Write an explicit rule for the arithmetic sequence that represents this situation, and use it to find how many miles Abby will run during her twelfth week of training.

A) Rule: Miles = 15 + 2(n - 1), Twelfth week: 39 miles
B) Rule: Miles = 15 + 2n, Twelfth week: 39 miles
C) Rule: Miles = 15 - 2n, Twelfth week: 3 miles
D) Rule: Miles = 15 - 2(n - 1), Twelfth week: 3 miles

Answer 1

The arithmetic sequence representing Abby's weekly training mileage is Miles = 15 + 2(n - 1). Using this rule for the twelfth week, she is expected to run 37 miles, suggesting a possible mismatch with the provided answer options.

Step-by-step explanation:

The subject question involves creating an explicit rule for an arithmetic sequence and determining the number of miles Abby will run during her twelfth week of training. To find this, we start with the initial amount of miles run in the first week and add the common difference (2 miles) multiplied by the number of weeks minus 1.

The explicit rule for the arithmetic sequence is Miles = 15 + 2(n - 1), where 'n' represents the week number. So for the twelfth week, we calculate the miles Abby will run as follows: Miles = 15 + 2(12 - 1) = 15 + 2(11) = 15 + 22 = 37 miles. However, this result of 37 miles does not match any options provided, so there might be an error in the recorded options or in the process of calculating the number of miles for the twelfth week.