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2.3 Arithmetic Sequences (Due 10-25-22)

Last updated 3 months ago

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Day 2 10/24/22

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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.

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1.

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2.

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.

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3.

What does f(1) mean?

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4.

What does f(n) mean?

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5.

What does d mean?

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6.

What does n mean?

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7.

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

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8.

Practice:
Complete the Arithmetic Sequence Example 1

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9.

Practice:
Complete the Arithmetic Sequence Example 2

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10.

Practice:
Graph the Arithmetic Sequence Example 1

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11.

Practice:
Graph the Arithmetic Sequence Example 2

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12.

What is the first term of this arithmetic sequence?

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13.

What is the common difference of this arithmetic sequence?

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14.

What is the explicit rule of this arithmetic sequence?

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15.

What is the explicit rule of this arithmetic sequence?

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16.

What is the explicit rule of this arithmetic sequence?

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17.

What is the explicit rule of this arithmetic sequence?

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18.

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19.

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40.

What is the explicit rule of this arithmetic sequence?

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41.

Find the first 4 terms of this arithmetic sequence:

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42.

Find the first 4 terms of this arithmetic sequence:

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43.

Find the 12th term of this arithmetic sequence:

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44.

Find the 9th term of this arithmetic sequence:

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45.

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46.

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47.

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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.

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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?

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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.

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51.

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

-6

6

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52.

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

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53.

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

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54.

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

Day 2 10/20/22

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20.

Find the next three terms of each sequence.

3, 7, 11, 15, , ,

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21.

Find the next three terms of each sequence.

22, 20, 18, 16, , ,

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22.

Find the next three terms of each sequence.

-2, -5, -8, -11, , ,

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23.

Find the first term and common difference in this sequence:

1, 3, 5, 7, ...

a₁=

d=

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24.

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

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25.

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

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26.

Find the first term and common difference in this sequence:

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

a₁=

d=

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27.

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

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28.

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

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29.

Find the first term and common difference in this sequence:

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

a₁=

d=

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30.

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

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31.

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

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32.

Find the first term and common difference in this sequence:

7, 13, 19, 25, ...

a₁=

d=

7, 13, 19, 25, ...

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33.

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

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34.

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

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35.

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

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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?

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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.

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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?

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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?