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2.3 Arithmetic Sequences (Due 10-25-22)

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A.SSE.1.a
F.BF.1.a
F.IF.3
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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.

Question 1
1.


Question 2
2.

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.
Question 3
3.


What does f(1) mean?

Question 4
4.


What does f(n) mean?

Question 5
5.


What does d mean?

Question 6
6.


What does n mean?

Question 7
7.

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


Question 8
8.

Practice:
Complete the Arithmetic Sequence Example 1

Question 9
9.

Practice:
Complete the Arithmetic Sequence Example 2

Question 10
10.

Practice:
Graph the Arithmetic Sequence Example 1

Question 11
11.

Practice:
Graph the Arithmetic Sequence Example 2

Question 12
12.

What is the first term of this arithmetic sequence?

Question 13
13.

What is the common difference of this arithmetic sequence?

Question 14
14.

What is the explicit rule of this arithmetic sequence?

Question 15
15.

What is the explicit rule of this arithmetic sequence?


Question 16
16.

What is the explicit rule of this arithmetic sequence?


Question 17
17.

What is the explicit rule of this arithmetic sequence?



Question 18
18.

Question 19
19.


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Day 2 10/24/22

Question 40
40.

What is the explicit rule of this arithmetic sequence?




Question 41
41.

Find the first 4 terms of this arithmetic sequence:


_______ _______ _______ _______


Question 42
42.

Find the first 4 terms of this arithmetic sequence:


_______ _______ _______ _______


Question 43
43.

Find the 12th term of this arithmetic sequence:


Question 44
44.

Find the 9th term of this arithmetic sequence:


Question 45
45.


Question 46
46.


Question 47
47.


Question 48
48.

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.

Question 49
49.

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?


Question 50
50.

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.

Question 51
51.

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

Question 52
52.

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

Question 53
53.

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


Question 54
54.

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



Day 2 10/20/22




Question 20
20.
Find the next three terms of each sequence.




3, 7, 11, 15, _______ ,_______ ,_______
Question 21
21.
Find the next three terms of each sequence.




22, 20, 18, 16, _______ ,_______ ,_______
Question 22
22.
Find the next three terms of each sequence.




-2, -5, -8, -11, _______ ,_______ ,_______
Question 23
23.
Find the first term and common difference in this sequence:

1, 3, 5, 7, ...

a₁=_______

d=_______


Question 24
24.

Write the explicit formula to find the nᵗʰ term of this sequence (you can use either notation):

1, 3, 5, 7, ...

Question 25
25.

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:

1, 3, 5, 7, ...


Question 26
26.
Find the first term and common difference in this sequence:

-1, -4, -7, -10, ...

a₁=_______

d=_______


Question 27
27.

Write an equation to find the nᵗʰ term of this sequence (you can use either notation):

-1, -4, -7, -10, ...

Question 28
28.

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:

-1, -4, -7, -10, ...

Question 29
29.
Find the first term and common difference in this sequence:

-4, -9, -14, -19, ...

a₁=_______

d=_______


Question 30
30.

Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):

-4, -9, -14, -19, ...

Question 31
31.

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:


-4, -9, -14, -19, ...

Question 32
32.
Find the first term and common difference in this sequence:

7, 13, 19, 25, ...

a₁=_______

d=_______


7, 13, 19, 25, ...
Question 33
33.

Write an explicit formula to find the nᵗʰ term of this sequence (you can use either notation):

7, 13, 19, 25, ...

Question 34
34.

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:



7, 13, 19, 25, ...

Question 35
35.

Charlie deposited $115 in a savings account. Each week thereafter, he deposits $35 into the account.

Write a formula to represent this sequence.

Question 36
36.

Charlie deposited $115 in a savings account. Each week thereafter, he deposits $35 into the account.



How much total money has Charlie
deposited after 30 weeks?


Question 37
37.

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.


Question 38
38.

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?


Question 39
39.

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?