Algebra 1 4-7 Guided Practice: Arithmetic Sequences

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Solve It! A wooden post-and-rail fence with two rails is made as shown.
Find the number of pieces of wood needed to build a 4-section fence, a 5-section fence, and a 6-section fence. Not all items will be used.

24 pieces
26 pieces
27 pieces
20 pieces
16 pieces
13 pieces
19 pieces
25 pieces

4-section fence
5-section fence
6-section fence

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Take Note: Define sequence.

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Take Note: Define term of a sequence.

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 1 Got It?

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Take Note: Define arithmetic sequence.

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Take Note: Define common difference (of an arithmetic sequence).

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Take Note: Provide an example of an arithmetic sequence with a common difference of 3 that includes 5 terms.

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

TAKE NOTE Key Concept

Recursive Formula For an Arithmetic Sequence
The nth term of an arithmetic sequence with first term A(1) and common difference d is given by 

Take Note: General recursive formula for an arithmetic sequence: 

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5

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Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

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Problem 3 Got It? What is the 9th term of the arithmetic sequence?

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Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

…

10

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

10

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

…

10

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

10

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

…

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Problem 3 Got It? What is the 9th term of the arithmetic sequence?

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Problem 3 Got It? Reasoning: Is a recursive formula a useful way to find a value of an arithmetic sequence?
HINT: What if you want to find the 91st term in an arithmetic sequence?

Take Note: General explicit formula for an arithmetic sequence: 

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Take Note: Define explicit formula.

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Problem 4 Got It?

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Problem 4 Got It?

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Problem 5 Got It?

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Problem 5 Got It?

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Problem 6 Got It?

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Problem 6 Got It?

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Algebra 1 4-7 Guided Practice: Arithmetic Sequences

Solve It! A wooden post-and-rail fence with two rails is made as shown. Find the number of pieces of wood needed to build a 4-section fence, a 5-section fence, and a 6-section fence. Not all items will be used.

Take Note: Define sequence.

Take Note: Define term of a sequence.

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Take Note: Define arithmetic sequence.

Take Note: Define common difference (of an arithmetic sequence).

Take Note: Provide an example of an arithmetic sequence with a common difference of 3 that includes 5 terms.

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

Problem 3 Got It? Reasoning: Is a recursive formula a useful way to find a value of an arithmetic sequence? HINT: What if you want to find the 91st term in an arithmetic sequence?

Take Note: Define explicit formula.

Problem 4 Got It?

Problem 4 Got It?

Problem 5 Got It?

Problem 5 Got It?

Problem 6 Got It?

Problem 6 Got It?

Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Solve It! A wooden post-and-rail fence with two rails is made as shown. Find the number of pieces of wood needed to build a 4-section fence, a 5-section fence, and a 6-section fence. Not all items will be used.

Take Note: Define sequence.

Take Note: Define term of a sequence.

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Take Note: Define arithmetic sequence.

Take Note: Define common difference (of an arithmetic sequence).

Take Note: Provide an example of an arithmetic sequence with a common difference of 3 that includes 5 terms.

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Take Note: Define recursive formula.

Take Note: In a recursive formula, why is it important to define the first term of the sequence?

Take Note: In a recursive formula, what does n represent?

Take Note: In a recursive formula, what does A(n) represent?

Take Note: In a recursive formula, what does A(1) represent?

Take Note: In a recursive formula, what does d represent?

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

Problem 3 Got It? What is the 9th term of the arithmetic sequence?

Problem 3 Got It? Reasoning: Is a recursive formula a useful way to find a value of an arithmetic sequence? HINT: What if you want to find the 91st term in an arithmetic sequence?

Take Note: Define explicit formula.

Take Note: In an explicit formula, what does n represent?

Take Note: In an explicit formula, what does A(n) represent?

Take Note: In an explicit formula, what does A(1) represent?

Take Note: In an explicit formula, what does d represent?

Problem 4 Got It?

Problem 4 Got It?

Problem 5 Got It?

Problem 5 Got It?

Problem 6 Got It?

Problem 6 Got It?

Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Define recursive formula.

Take Note: In a recursive formula, why is it important to define the first term of the sequence?

Take Note: In a recursive formula, what does n represent?

Take Note: In a recursive formula, what does A(n) represent?

Take Note: In a recursive formula, what does A(1) represent?

Take Note: In a recursive formula, what does d represent?

Solve It! A wooden post-and-rail fence with two rails is made as shown.
Find the number of pieces of wood needed to build a 4-section fence, a 5-section fence, and a 6-section fence. Not all items will be used.

Problem 3 Got It? Reasoning: Is a recursive formula a useful way to find a value of an arithmetic sequence?
HINT: What if you want to find the 91st term in an arithmetic sequence?

Solve It! A wooden post-and-rail fence with two rails is made as shown.
Find the number of pieces of wood needed to build a 4-section fence, a 5-section fence, and a 6-section fence. Not all items will be used.

Problem 3 Got It? Reasoning: Is a recursive formula a useful way to find a value of an arithmetic sequence?
HINT: What if you want to find the 91st term in an arithmetic sequence?