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

Mar 13, 2025 by ADMIN 283 views

**The Sequence of Diesel Fuel Remaining in a Fuel Station's Tank**

Introduction

In this article, we will explore 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 will examine the sequence for the values of $n$ ranging from 1 to 7 and create a table to represent the number of gallons of diesel fuel remaining in the tank for each value of $n$ .

Understanding the Sequence

The sequence $a_n=12,000-200n$ is a linear sequence 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. The sequence is defined by the formula $a_n=12,000-200n$ , where $a_n$ represents the number of gallons of diesel fuel remaining in the tank after $n$ semi-truck owners have filled their tanks.

Calculating the Number of Gallons of Diesel Fuel Remaining

To calculate the number of gallons of diesel fuel remaining in the tank for each value of $n$ , we can plug in the values of $n$ into the formula $a_n=12,000-200n$ . Let's calculate the number of gallons of diesel fuel remaining in the tank for each value of $n$ from 1 to 7.

Calculating the Number of Gallons of Diesel Fuel Remaining for n = 1

For $n = 1$ , we can plug in the value of $n$ into the formula $a_n=12,000-200n$ to get:

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

So, after 1 semi-truck owner has filled their tank, there are 11,800 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons of Diesel Fuel Remaining for n = 2

For $n = 2$ , we can plug in the value of $n$ into the formula $a_n=12,000-200n$ to get:

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

So, after 2 semi-truck owners have filled their tanks, there are 11,600 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons of Diesel Fuel Remaining for n = 3

For $n = 3$ , we can plug in the value of $n$ into the formula $a_n=12,000-200n$ to get:

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

So, after 3 semi-truck owners have filled their tanks, there are 11,400 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons of Diesel Fuel Remaining for n = 4

For $n = 4$ , we can plug in the value of $n$ into the formula $a_n=12,000-200n$ to get:

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

So, after 4 semi-truck owners have filled their tanks, there are 11,200 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons of Diesel Fuel Remaining for n = 5

For $n = 5$ , we can plug in the value of $n$ into the formula $a_n=12,000-200n$ to get:

$a_5 = 12,000 - 200(5)$ $a_5 = 12,000 - 1,000$ $a_5 = 10,000$

So, after 5 semi-truck owners have filled their tanks, there are 10,000 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons of Diesel Fuel Remaining for n = 6

For $n = 6$ , we can plug in the value of $n$ into the formula $a_n=12,000-200n$ to get:

$a_6 = 12,000 - 200(6)$ $a_6 = 12,000 - 1,200$ $a_6 = 9,800$

So, after 6 semi-truck owners have filled their tanks, there are 9,800 gallons of diesel fuel remaining in the tank.

Calculating the Number of Gallons of Diesel Fuel Remaining for n = 7

For $n = 7$ , we can plug in the value of $n$ into the formula $a_n=12,000-200n$ to get:

$a_7 = 12,000 - 200(7)$ $a_7 = 12,000 - 1,400$ $a_7 = 9,600$

So, after 7 semi-truck owners have filled their tanks, there are 9,600 gallons of diesel fuel remaining in the tank.

Creating a Table to Represent the Number of Gallons of Diesel Fuel Remaining

Based on the calculations above, we can create a table to represent the number of gallons of diesel fuel remaining in the tank for each value of $n$ from 1 to 7.

n	Number of Gallons of Diesel Fuel Remaining
1	11,800
2	11,600
3	11,400
4	11,200
5	10,000
6	9,800
7	9,600

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 is the sequence defined?

A: The sequence is defined by the formula $a_n=12,000-200n$ , where $a_n$ represents the number of gallons of diesel fuel remaining in the tank after $n$ semi-truck owners have filled their tanks.

Q: What is the initial value of the sequence?

A: The initial value of the sequence is 12,000, which represents the number of gallons of diesel fuel remaining 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 of diesel fuel remaining in the tank decreases. This is because each semi-truck owner who fills their tank reduces the amount of diesel fuel remaining in the tank.

Q: What is the rate at which the sequence decreases?

A: The sequence decreases at a rate of 200 gallons per semi-truck owner.

Q: Can you provide an example of how to calculate the number of gallons of diesel fuel remaining in the tank for a given value of n?

A: Yes, for example, to calculate the number of gallons of diesel fuel remaining in the tank for $n=5$ , we can plug in the value of $n$ into the formula $a_n=12,000-200n$ to get:

$a_5 = 12,000 - 200(5)$ $a_5 = 12,000 - 1,000$ $a_5 = 10,000$

So, after 5 semi-truck owners have filled their tanks, there are 10,000 gallons of diesel fuel remaining in the tank.

Q: How can I use the sequence to determine the number of gallons of diesel fuel remaining in the tank for a given value of n?

A: To use the sequence to determine the number of gallons of diesel fuel remaining in the tank for a given value of $n$ , you can simply plug in the value of $n$ into the formula $a_n=12,000-200n$ and calculate the result.

Q: What is the maximum value of n for which the sequence is defined?

A: The maximum value of $n$ for which the sequence is defined is 7, since the sequence is only defined for values of $n$ from 1 to 7.

Q: Can I use the sequence to determine the number of gallons of diesel fuel remaining in the tank for values of n greater than 7?

A: No, the sequence is only defined for values of $n$ from 1 to 7, so you cannot use the sequence to determine the number of gallons of diesel fuel remaining in the tank for values of $n$ greater than 7.

Q: What is the minimum value of n for which the sequence is defined?

A: The minimum value of $n$ for which the sequence is defined is 1, since the sequence is only defined for values of $n$ from 1 to 7.