Question

A recovering heart attack patient is told to get on a regular walking program. The patient is told to walk a distance of 5 km the first week, 8 km the second week, 11 km the third week and so on for a period of 10 weeks. At that point the patient is to maintain the distance walked during the 10th week. How far will the patient walk during the 10th week? a. Is the sequence arithmetic or geometric? Explain your answer.

Answer 1

The sequence in this scenario is arithmetic, with the patient increasing their distance walked by 3 km each week. Using the formula for the nth term of an arithmetic sequence, the patient will walk a distance of 32 km during the 10th week.

Step-by-step explanation:

The sequence in this case is arithmetic. This can be determined by observing that the difference between the distances walked each week is consistent. In this case, the difference is 3 km, as the patient increases their distance by 3 km each week.

To find out how far the patient will walk during the 10th week, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

Where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

Given that the first term is 5 km, the common difference is 3 km, and we want to find the 10th term, we can substitute the values into the formula:

a10 = 5 + (10-1)3

a10 = 5 + 9 * 3

a10 = 5 + 27

a10 = 32

Therefore, the patient will walk a distance of 32 km during the 10th week.

Answer 2

he is to maintain waling 31km a week