The Sequence A N = 12 , 000 − 200 N A_n = 12,000 - 200n A N ​ = 12 , 000 − 200 N Represents The Number Of Gallons Of Diesel Fuel Remaining In A Fuel Station's Tank After N N N Semi-truck Owners Have Filled Their Tanks. If 1 ≤ N ≤ 7 1 \leq N \leq 7 1 ≤ N ≤ 7 , Which Table Represents The

Introduction

The sequence $a_n = 12,000 - 200n$ represents the number of gallons of diesel fuel remaining in a fuel station's tank after $n$ semi-truck owners have filled their tanks. This sequence is a linear function that decreases by 200 gallons for each semi-truck owner who fills their tank. In this article, we will explore the sequence and create a table to represent the number of gallons of diesel fuel remaining in the tank for $1 \leq n \leq 7$.

Understanding the Sequence

The sequence $a_n = 12,000 - 200n$ is a linear function that can be broken down into two parts: the initial value of 12,000 gallons and the decrease of 200 gallons for each semi-truck owner who fills their tank. The sequence starts at 12,000 gallons and decreases by 200 gallons for each value of $n$.

Calculating the Number of Gallons Remaining

To calculate the number of gallons remaining in the tank for each value of $n$, we can plug in the values of $n$ into the sequence $a_n = 12,000 - 200n$. Let's calculate the number of gallons remaining for $n = 1, 2, 3, 4, 5, 6, 7$.

Calculating the Number of Gallons Remaining for n = 1

For $n = 1$, we plug in the value of $n$ into the sequence $a_n = 12,000 - 200n$.

$a_1 = 12,000 - 200(1)$ $a_1 = 12,000 - 200$ $a_1 = 11,800$

So, for $n = 1$, there are 11,800 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons Remaining for n = 2

For $n = 2$, we plug in the value of $n$ into the sequence $a_n = 12,000 - 200n$.

$a_2 = 12,000 - 200(2)$ $a_2 = 12,000 - 400$ $a_2 = 11,600$

So, for $n = 2$, there are 11,600 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons Remaining for n = 3

For $n = 3$, we plug in the value of $n$ into the sequence $a_n = 12,000 - 200n$.

$a_3 = 12,000 - 200(3)$ $a_3 = 12,000 - 600$ $a_3 = 11,400$

So, for $n = 3$, there are 11,400 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons Remaining for n = 4

For $n = 4$, we plug in the value of $n$ into the sequence $a_n = 12,000 - 200n$.

$a_4 = 12,000 - 200(4)$ $a_4 = 12,000 - 800$ $a_4 = 11,200$

So, for $n = 4$, there are 11,200 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons Remaining for n = 5

For $n = 5$, we plug in the value of $n$ into the sequence $a_n = 12,000 - 200n$.

$a_5 = 12,000 - 200(5)$ $a_5 = 12,000 - 1,000$ $a_5 = 11,000$

So, for $n = 5$, there are 11,000 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons Remaining for n = 6

For $n = 6$, we plug in the value of $n$ into the sequence $a_n = 12,000 - 200n$.

$a_6 = 12,000 - 200(6)$ $a_6 = 12,000 - 1,200$ $a_6 = 10,800$

So, for $n = 6$, there are 10,800 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons Remaining for n = 7

For $n = 7$, we plug in the value of $n$ into the sequence $a_n = 12,000 - 200n$.

$a_7 = 12,000 - 200(7)$ $a_7 = 12,000 - 1,400$ $a_7 = 10,600$

So, for $n = 7$, there are 10,600 gallons of diesel fuel remaining in the tank.

Creating a Table to Represent the Sequence

Now that we have calculated the number of gallons remaining in the tank for each value of $n$, we can create a table to represent the sequence.

$n$	Number of Gallons Remaining
1	11,800
2	11,600
3	11,400
4	11,200
5	11,000
6	10,800
7	10,600

Conclusion

$$$$$$$$

Q: What is the sequence $a_n = 12,000 - 200n$?

A: The sequence $a_n = 12,000 - 200n$ represents the number of gallons of diesel fuel remaining in a fuel station's tank after $n$ semi-truck owners have filled their tanks.

Q: How does the sequence work?

A: The sequence starts at 12,000 gallons and decreases by 200 gallons for each semi-truck owner who fills their tank. This means that for each value of $n$, the number of gallons remaining in the tank decreases by 200 gallons.

Q: What is the initial value of the sequence?

A: The initial value of the sequence is 12,000 gallons, which represents the number of gallons of diesel fuel in the tank before any semi-truck owners have filled their tanks.

Q: How does the sequence change as $n$ increases?

A: As $n$ increases, the number of gallons remaining in the tank decreases by 200 gallons for each semi-truck owner who fills their tank. This means that the sequence decreases linearly as $n$ increases.

Q: Can I use the sequence to determine the number of gallons remaining in the tank for any value of $n$?

A: Yes, you can use the sequence to determine the number of gallons remaining in the tank for any value of $n$ between 1 and 7. Simply plug in the value of $n$ into the sequence $a_n = 12,000 - 200n$ to find the number of gallons remaining in the tank.

Q: What happens if $n$ is greater than 7?

A: If $n$ is greater than 7, the sequence will result in a negative number, which is not possible in this context. This means that the sequence is only valid for values of $n$ between 1 and 7.

Q: Can I use the sequence to determine the number of gallons of diesel fuel that need to be added to the tank to reach a certain level?

A: Yes, you can use the sequence to determine the number of gallons of diesel fuel that need to be added to the tank to reach a certain level. Simply subtract the number of gallons remaining in the tank from the desired level to find the number of gallons that need to be added.

Q: What are some real-world applications of the sequence?

A: The sequence has several real-world applications, including:

• Determining the number of gallons of diesel fuel remaining in a fuel station's tank after a certain number of semi-truck owners have filled their tanks.
• Calculating the number of gallons of diesel fuel that need to be added to the tank to reach a certain level.
• Optimizing fuel delivery routes to minimize the number of gallons of diesel fuel that need to be transported.

Q: Can I use the sequence to model other real-world scenarios?

A: Yes, you can use the sequence to model other real-world scenarios, including:

• Modeling the number of gallons of gasoline remaining in a car's tank after a certain number of miles have been driven.
• Calculating the number of gallons of diesel fuel that need to be added to a generator to reach a certain level.
• Optimizing fuel consumption in industrial settings, such as factories or power plants.

Conclusion

In this article, we answered some frequently asked questions about the sequence $a_n = 12,000 - 200n$ that represents the number of gallons of diesel fuel remaining in a fuel station's tank after $n$ semi-truck owners have filled their tanks. We hope that this article has provided you with a better understanding of the sequence and its applications.