An arithmetic sequence is a sequence in which the difference between consecutive terms is constant. Let's analyze each option:

1. The cost of n gallons of gas to pump up a truck: The cost would depend on the price per gallon of gas. Since the cost increases at a constant rate for each additional gallon, this could be described using an arithmetic sequence.

2. The number of exams a professor has left to grade on the nth week of a semester: This depends on how many exams are graded each week, which could vary, so this is not guaranteed to follow an arithmetic sequence.

3. The cost of n donuts at Sara's Donut shop: Assuming each donut costs the same, the total cost would increase at a constant rate as more donuts are purchased, making this an arithmetic sequence.

4. The number of kilometers left to run in n minutes of a marathon: The number of kilometers left decreases as the runner progresses. However, this decrease might not be at a constant rate depending on the runner's speed, so it is not guaranteed to follow an arithmetic sequence.

Correct Answers:

• The cost of n gallons of gas to pump up a truck
• The cost of n donuts at Sara's Donut shop

Would you like further details on this? Here are some related questions:

1. What is the general formula for an arithmetic sequence?
2. How can we differentiate between an arithmetic and geometric sequence?
3. What real-life scenarios represent geometric sequences instead?
4. How do we find the nth term of an arithmetic sequence?
5. What is the significance of the common difference in arithmetic sequences?

Tip: In an arithmetic sequence, the difference between consecutive terms is constant—this is known as the "common difference."