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.

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

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

F.IF.3

F.LE.2

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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?

A

B

C

D

F.BF.1.a

F.IF.3

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Problem 1 Got It?

A

B

C

D

F.BF.1.a

F.IF.3

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Problem 1 Got It?

A

B

C

D

F.BF.1.a

F.IF.3

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Problem 1 Got It?

A

B

C

D

F.BF.1.a

F.IF.3

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Take Note: Define arithmetic sequence.

10

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.

10

Problem 2 Got It?

A

B

C

D

F.BF.1.a

F.IF.3

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Problem 2 Got It?

A

B

C

D

F.BF.1.a

F.IF.3

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Problem 2 Got It?

A

B

C

D

F.BF.1.a

F.IF.3

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Problem 2 Got It?

A

B

C

D

F.BF.1.a

F.IF.3

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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Take Note: Define recursive formula.

5

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

A(n) = A(n - 1) + 4; \ \ \ A(1) = 3

A(n) = A(n - 1) + 5; \ \ \ A(1) = 3

A(n) = A(n - 1) + 3; \ \ \ A(1) = 3

A(n) = A(n - 1) + 6; \ \ \ A(1) = 3

A.SSE.1.a

F.BF.1.a

…

10

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

A(9) = 35

A(9) = 51

A(9) = 27

A(9) = 9

F.BF.1.a

F.IF.3

F.LE.2

10

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

A(n) = A(n - 1) + 18; \ \ \ A(1) = 23

A(n) = A(n - 1) + 12; \ \ \ A(1) = 23

A(n) = A(n - 1) + 15; \ \ \ A(1) = 23

A(n) = A(n - 1) + 3; \ \ \ A(1) = 23

A.SSE.1.a

F.BF.1.a

…

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

A(9) = 81

A(9) = 119

A(9) = 107

A(9) = 151

F.BF.1.a

F.IF.3

10

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

A(n) = A(n - 1) + 0.5; \ \ \ A(1) = 7.3

A(n) = A(n - 1) + 1.5; \ \ \ A(1) = 7.3

A(n) = A(n - 1) + 1; \ \ \ A(1) = 7.3

A(n) = A(n - 1) + 2.5; \ \ \ A(1) = 7.3

A.SSE.1.a

F.BF.1.a

…

10

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

A(9) = 9.3

A(9) = 11.3

A(9) = 10.8

A(9) = 11.1

F.BF.1.a

F.IF.3

10

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

A(n) = A(n - 1) + 9; \ \ \ A(1) = 97

A(n) = A(n - 1) + 3; \ \ \ A(1) = 97

A(n) = A(n - 1) - 9; \ \ \ A(1) = 97

A(n) = A(n - 1) - 3; \ \ \ A(1) = 97

A.SSE.1.a

F.BF.1.a

…

10

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

A(9) = 30

A(9) = 35

A(9) = 25

A(9) = 20

F.BF.1.a

F.IF.3

10

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:

10

Take Note: Define explicit formula.

5

10

Problem 4 Got It?

A

B

C

D

A.SSE.1.a

F.BF.1.a

…

10

Problem 4 Got It?

A

B

C

D

A.SSE.1.a

F.IF.3

10

Problem 5 Got It?

A

B

C

D

A.SSE.1.a

F.BF.1.a

…

10

Problem 5 Got It?

A

B

C

D

A.SSE.1.a

F.BF.1.a

…

10

Problem 6 Got It?

A

B

C

D

A.SSE.1.a

F.BF.1.a

…

10

Problem 6 Got It?

A

B

C

D

A.SSE.1.a

F.BF.1.a

…

10

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?

Take Note: Define recursive formula.

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: 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?