Which of the following could be described using an arithmetic sequence?
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Multiple Choice Answers
The cost of n gallons of gas to pump up a truck.
The number of exams a professor has left to grade on the nth week of a semester.
The cost of n donuts at Sara's Donut shop.
The number of kilometers left to run in n minutes of a marathon.

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."

Which of the following could be described using an arithmetic sequence?
1. The cost of n gallons of gas to pump up a truck.
2. The number of exams a professor has left to grade on the nth week of a semester.
3. The cost of n donuts at Sara's Donut shop.
4. The number of kilometers left to run in n minutes of a marathon.

Explore how to identify arithmetic sequences with real-world examples, including the cost of n gallons of gas and n donuts. Learn the general formula for arithmetic sequences and understand the properties of linear relationships. Suitable for students in Grades 6-8.

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