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 10/5/23
Exploration
Triangle Problem: Consider the relationship between the number of triangles in each figure in the diagram below and the perimeter of each figure.
Required
20 points
20
Question 1
1.
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)
Required
5 points
5
Question 2
2.
Triangle Problem:
What is happening to the perimeter of the shape everytime another traingle is added?
Required
5 points
5
Question 3
3.
Triangle Problem:
Make a prediction. What would be the perimeter of 7 triangles joined together?
Application Problem. Consider the relationship represented in the table below.
Required
10 points
10
Question 4
4.
Application Problem:
Describe the relationship of this function using words.
Required
20 points
20
Question 5
5.
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.
Required
10 points
10
Question 6
6.
Application Problem:
Make a prediction. What will be the output of the 6th input?
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5 points
5
Question 7
7.
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5 points
5
Question 8
8.
What is the pattern of this sequence?
Any term in an arithmetic sequence is equal to the first term plus a term number minus 1 times the common difference.
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2 points
2
Question 9
9.
What does f(1) mean?
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2 points
2
Question 10
10.
What does f(n) mean?
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2 points
2
Question 11
11.
What does d mean?
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2 points
2
Question 12
12.
What does n mean?
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10 points
10
Question 13
13.
Use the following situation involving an arithmetic sequence to construct a explicit rule.
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10 points
10
Question 14
14.
Write the explicit rule for this arithmetic sequence:
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10 points
10
Question 15
15.
Write the explicit rule for this arithmetic sequence:
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10 points
10
Question 16
16.
Graph the Arithmetic Sequence Example 1
Required
10 points
10
Question 17
17.
Graph the Arithmetic Sequence Example 2
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20 points
20
Question 18
18.
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.
Required
20 points
20
Question 19
19.
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.
Required
2 points
2
Question 20
20.
What is the first term of this arithmetic sequence?
5 points
5
Question 21
21.
What is the common difference of this arithmetic sequence?
Required
10 points
10
Question 22
22.
What is the explicit rule of this arithmetic sequence?
Required
10 points
10
Question 23
23.
What is the explicit rule of this arithmetic sequence?
Required
10 points
10
Question 24
24.
What is the explicit rule of this arithmetic sequence?
Required
10 points
10
Question 25
25.
What is the explicit rule of this arithmetic sequence?
Required
20 points
20
Question 26
26.
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10 points
10
Question 27
27.
Day 2 10/11/23
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15 points
15
Question 28
28.
Find the next three terms of each sequence.
3, 7, 11, 15, _______ ,_______ ,_______
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15 points
15
Question 29
29.
Find the next three terms of each sequence.
22, 20, 18, 16, _______ ,_______ ,_______
Required
15 points
15
Question 30
30.
Find the next three terms of each sequence.
-2, -5, -8, -11, _______ ,_______ ,_______
Required
10 points
10
Question 31
31.
Find the first term and common difference in this sequence:
1, 3, 5, 7, ...
a₁=_______
d=_______
Required
10 points
10
Question 32
32.
Write the explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
1, 3, 5, 7, ...
Required
10 points
10
Question 33
33.
Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
1, 3, 5, 7, ...
Required
10 points
10
Question 34
34.
Find the first term and common difference in this sequence:
-1, -4, -7, -10, ...
a₁=_______
d=_______
Required
10 points
10
Question 35
35.
Write an equation to find the nᵗʰ term of this sequence (you can use either notation):
-1, -4, -7, -10, ...
Required
10 points
10
Question 36
36.
Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
-1, -4, -7, -10, ...
Required
10 points
10
Question 37
37.
Find the first term and common difference in this sequence:
-4, -9, -14, -19, ...
a₁=_______
d=_______
Required
10 points
10
Question 38
38.
Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
-4, -9, -14, -19, ...
Required
10 points
10
Question 39
39.
Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
-4, -9, -14, -19, ...
Required
5 points
5
Question 40
40.
Find the first term and common difference in this sequence:
7, 13, 19, 25, ...
a₁=_______
d=_______
7, 13, 19, 25, ...
Required
10 points
10
Question 41
41.
Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):
7, 13, 19, 25, ...
Required
10 points
10
Question 42
42.
Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:
7, 13, 19, 25, ...
Required
10 points
10
Question 43
43.
Charlie deposited $115 in a savings account. Each week after that, he deposits $35 into the account.
Write a formula to represent this sequence.
Required
10 points
10
Question 44
44.
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?
Required
10 points
10
Question 45
45.
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.
Required
10 points
10
Question 46
46.
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?
Required
10 points
10
Question 47
47.
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?
Day 2 10/24/22
Required
10 points
10
Question 48
48.
What is the explicit rule of this arithmetic sequence?
Required
20 points
20
Question 49
49.
Find the first 4 terms of this arithmetic sequence:
_______ _______ _______ _______
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20 points
20
Question 50
50.
Find the first 4 terms of this arithmetic sequence:
_______ _______ _______ _______
Required
10 points
10
Question 51
51.
Find the 12th term of this arithmetic sequence:
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10 points
10
Question 52
52.
Find the 9th term of this arithmetic sequence:
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10 points
10
Question 53
53.
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10 points
10
Question 54
54.
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10 points
10
Question 55
55.
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10 points
10
Question 56
56.
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.
Required
10 points
10
Question 57
57.
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?
Required
10 points
10
Question 58
58.
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.
Required
3 points
3
Question 59
59.
Vocabulary: Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Is the common difference 6 or -6?
Required
5 points
5
Question 60
60.
Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Write the explicit rule for this arithmetic sequence.
Required
10 points
10
Question 61
61.
Error Analysis:
Describe the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28, ...
Required
10 points
10
Question 62
62.
Error Analysis:
Find the real the tenth term of the arithmetic sequence 4, 12, 20, 28, ...