Constructing Arithmetic Sequences

Essential Question: What is an arithmetic sequence?

Learning Target: Students will be able to create an explicit rule describing an arithmetic sequence and use it to calculate any term in that sequence.

Complete the entire document and show all work for credit.

Day 1 10/23/25

Exploration

Triangle Problem: Consider the relationship between the number of triangles in each figure in the diagram below and the perimeter of each figure.

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Obavezno

20

Triangle Problem:
Represent this relationship with a table and a graph.
1) Use the table to show the relationship between the number of triangles and the perimeter of the shape created.
2) Use the table data to create a graph of the data.
3) Use the data to make predictions
For instance 1 triangle has a perimeter of 10, so the a point will placed (1,10)

Obavezno

5

Triangle Problem:
What is happening to the perimeter of the shape every time another triangle is added?

Obavezno

5

A.REI.10

Application Problem. Consider the relationship represented in the table below.

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Obavezno

10

Application Problem:
Describe the relationship of this function using words.

Obavezno

20

Application Problem:
Use the table data to create a graph.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Obavezno

10

Application Problem:
Make a prediction. What will be the output of the 6th input?

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Obavezno

5

Obavezno

5

What is the pattern of this sequence?

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Any term in an arithmetic sequence is equal to the first term plus a term number minus 1 times the common difference.

Obavezno

2

What does f(1) mean?

Obavezno

2

What does f(n) mean?

Obavezno

2

What does d mean?

Obavezno

2

What does n mean?

Obavezno

10

Use the following situation involving an arithmetic sequence to construct a explicit rule.

10

Obavezno

10

Write the explicit rule for this arithmetic sequence:

Obavezno

10

Graph the Arithmetic Sequence Example 1

Obavezno

10

Graph the Arithmetic Sequence Example 2

Obavezno

20

What is the graph of this function?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

A.REI.10

F.IF.5

N.Q.1

Obavezno

20

The function rule below represents the total weight W, in pounds, of a spa that contains g gallons of water. What is a reasonable graph of the function rule, given that the capacity of the spa is 250 gal?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

A.REI.10

F.IF.5

N.Q.1

Obavezno

2

What is the first term of this arithmetic sequence?

5

What is the common difference of this arithmetic sequence?

Obavezno

10

What is the explicit rule of this arithmetic sequence?

Obavezno

10

What is the explicit rule of this arithmetic sequence?

Obavezno

10

What is the explicit rule of this arithmetic sequence?

Obavezno

10

What is the explicit rule of this arithmetic sequence?

Obavezno

20

Obavezno

10

Obavezno

15

Obavezno

15

Obavezno

15

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

5

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Obavezno

10

Day 3 10/27/25

Obavezno

10

What is the explicit rule of this arithmetic sequence?

Obavezno

20

Obavezno

20

Obavezno

10

Find the 12th term of this arithmetic sequence:

Obavezno

10

Find the 9th term of this arithmetic sequence:

Obavezno

10

Obavezno

10

Obavezno

10

You start a side hustle on OfferUp. If you need to ship something across the country, it cost 5.75 for the first pound and $0.75 for each additional pound. Construct an explicit rule that represents this situation.

Obavezno

10

You start a side hustle on OfferUp. If you need to ship something across the country, it cost 5.75 for the first pound and $0.75 for each additional pound.
How much would it cost to ship a pair of 30lb weights?

Obavezno

10

Luigi borrows 960 gold coins from Princess Peach to fix his go-kart. He promises to pay her back 120 gold coins every month. Construct an explicit rule that represents this situation.

Obavezno

3

Vocabulary: Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Is the common difference 6 or -6?

6

-6

A.SSE.1.a

F.BF.1.a

F.IF.3

Obavezno

5

Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Write the explicit rule for this arithmetic sequence.

Obavezno

10

Error Analysis:
Describe the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28, ...

Obavezno

10

2.3 Arithmetic Sequences (Due 10-29-24)

Day 1 10/23/25

Exploration

Day 3 10/27/25

2.3 Arithmetic Sequences (Due 10-29-24)

Constructing Arithmetic Sequences

Essential Question: What is an arithmetic sequence?

Learning Target: Students will be able to create an explicit rule describing an arithmetic sequence and use it to calculate any term in that sequence.

Complete the entire document and show all work for credit.

Day 1 10/23/25

Exploration

Triangle Problem: What is happening to the perimeter of the shape every time another triangle is added?

Application Problem:Describe the relationship of this function using words.

Application Problem:Use the table data to create a graph.Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Application Problem:Make a prediction. What will be the output of the 6th input?

What is the pattern of this sequence?

What does f(1) mean?

What does f(n) mean?

What does d mean?

What does n mean?

Use the following situation involving an arithmetic sequence to construct a explicit rule.

Write the explicit rule for this arithmetic sequence:

Graph the Arithmetic Sequence Example 1

Graph the Arithmetic Sequence Example 2

What is the graph of this function?Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

What is the first term of this arithmetic sequence?

What is the common difference of this arithmetic sequence?

What is the explicit rule of this arithmetic sequence?

What is the explicit rule of this arithmetic sequence?

What is the explicit rule of this arithmetic sequence?

What is the explicit rule of this arithmetic sequence?

Day 3 10/27/25

What is the explicit rule of this arithmetic sequence?

Find the 12th term of this arithmetic sequence:

Find the 9th term of this arithmetic sequence:

You start a side hustle on OfferUp. If you need to ship something across the country, it cost 5.75 for the first pound and $0.75 for each additional pound. Construct an explicit rule that represents this situation.

You start a side hustle on OfferUp. If you need to ship something across the country, it cost 5.75 for the first pound and $0.75 for each additional pound. How much would it cost to ship a pair of 30lb weights?

Luigi borrows 960 gold coins from Princess Peach to fix his go-kart. He promises to pay her back 120 gold coins every month. Construct an explicit rule that represents this situation.

Vocabulary: Consider the following arithmetic sequence: 25, 19, 13, 7, ... Is the common difference 6 or -6?

Consider the following arithmetic sequence: 25, 19, 13, 7, ... Write the explicit rule for this arithmetic sequence.

Error Analysis: Describe the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28, ...

Error Analysis: Find the real the tenth term of the arithmetic sequence 4, 12, 20, 28, ...

Constructing Arithmetic Sequences

Essential Question: What is an arithmetic sequence?

Learning Target: Students will be able to create an explicit rule describing an arithmetic sequence and use it to calculate any term in that sequence.

Complete the entire document and show all work for credit.

Triangle Problem: What is happening to the perimeter of the shape every time another triangle is added?

Triangle Problem: Make a prediction. What would be the perimeter of 7 triangles joined together?

Application Problem:Describe the relationship of this function using words.

Application Problem:Use the table data to create a graph.Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Application Problem:Make a prediction. What will be the output of the 6th input?

What is the pattern of this sequence?

What does f(1) mean?

What does f(n) mean?

What does d mean?

What does n mean?

Use the following situation involving an arithmetic sequence to construct a explicit rule.

Write the explicit rule for this arithmetic sequence:

Graph the Arithmetic Sequence Example 1

Graph the Arithmetic Sequence Example 2

What is the graph of this function?Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

What is the first term of this arithmetic sequence?

What is the common difference of this arithmetic sequence?

What is the explicit rule of this arithmetic sequence?

What is the explicit rule of this arithmetic sequence?

What is the explicit rule of this arithmetic sequence?

What is the explicit rule of this arithmetic sequence?

Day 2 10/24/25

Write the explicit formula to find the nᵗʰ term of this sequence (you can use either notation):1, 3, 5, 7, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:1, 3, 5, 7, ...

Write an equation to find the nᵗʰ term of this sequence (you can use either notation):-1, -4, -7, -10, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:-1, -4, -7, -10, ...

Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):-4, -9, -14, -19, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:-4, -9, -14, -19, ...

Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):7, 13, 19, 25, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:7, 13, 19, 25, ...

Charlie deposited $115 in a savings account. Each week after that, he deposits $35 into the account.Write a formula to represent this sequence.

Charlie deposited $115 in a savings account. Each week after that, he deposits $35 into the account.How much total money has Charliedeposited after 30 weeks?

As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water.Write a formula to represent this sequence.

As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water.How much water is remaining after shehands out the 14ᵗʰ cup?

Triangle Problem:
What is happening to the perimeter of the shape every time another triangle is added?

Application Problem:
Describe the relationship of this function using words.

Application Problem:
Use the table data to create a graph.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Application Problem:
Make a prediction. What will be the output of the 6th input?

What is the graph of this function?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

You start a side hustle on OfferUp. If you need to ship something across the country, it cost 5.75 for the first pound and $0.75 for each additional pound.
How much would it cost to ship a pair of 30lb weights?

Vocabulary: Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Is the common difference 6 or -6?

Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Write the explicit rule for this arithmetic sequence.

Error Analysis:
Describe the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28, ...

Error Analysis:
Find the real the tenth term of the arithmetic sequence 4, 12, 20, 28, ...

Triangle Problem:
What is happening to the perimeter of the shape every time another triangle is added?

Triangle Problem:
Make a prediction. What would be the perimeter of 7 triangles joined together?

Application Problem:
Describe the relationship of this function using words.

Application Problem:
Use the table data to create a graph.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Application Problem:
Make a prediction. What will be the output of the 6th input?

What is the graph of this function?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Write the explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
1, 3, 5, 7, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
1, 3, 5, 7, ...

Write an equation to find the nᵗʰ term of this sequence (you can use either notation):
-1, -4, -7, -10, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
-1, -4, -7, -10, ...

Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
-4, -9, -14, -19, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
-4, -9, -14, -19, ...

Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
7, 13, 19, 25, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
7, 13, 19, 25, ...

Charlie deposited $115 in a savings account. Each week after that, he deposits $35 into the account.
Write a formula to represent this sequence.

Charlie deposited $115 in a savings account. Each week after that, he deposits $35 into the account.
How much total money has Charlie
deposited after 30 weeks?

As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water.
Write a formula to represent this sequence.

As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water.
How much water is remaining after she
hands out the 14ᵗʰ cup?

As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water.
How many cups can she fill up before she runs out of water?

You start a side hustle on OfferUp. If you need to ship something across the country, it cost 5.75 for the first pound and $0.75 for each additional pound.
How much would it cost to ship a pair of 30lb weights?

Vocabulary: Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Is the common difference 6 or -6?

Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Write the explicit rule for this arithmetic sequence.

Error Analysis:
Describe the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28, ...

Error Analysis:
Find the real the tenth term of the arithmetic sequence 4, 12, 20, 28, ...

Triangle Problem:
Make a prediction. What would be the perimeter of 7 triangles joined together?

Write the explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
1, 3, 5, 7, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
1, 3, 5, 7, ...

Write an equation to find the nᵗʰ term of this sequence (you can use either notation):
-1, -4, -7, -10, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
-1, -4, -7, -10, ...

Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
-4, -9, -14, -19, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
-4, -9, -14, -19, ...

Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
7, 13, 19, 25, ...

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
7, 13, 19, 25, ...

Charlie deposited $115 in a savings account. Each week after that, he deposits $35 into the account.
Write a formula to represent this sequence.

Charlie deposited $115 in a savings account. Each week after that, he deposits $35 into the account.
How much total money has Charlie
deposited after 30 weeks?

As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water.
Write a formula to represent this sequence.

As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water.
How much water is remaining after she
hands out the 14ᵗʰ cup?

As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is 4 ounces. She begins practice with a 128-ounce cooler of water.
How many cups can she fill up before she runs out of water?