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Algebra 1 4-7 Arithmetic Sequences
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by Matthew Richardson
| 37 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
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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.
• 4-section fence
• 5-section fence
• 6-section fence
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Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

A(n) = A(n - 1) + 3; A(1) = 3
A(n) = A(n - 1) + 4; A(1) = 3
A(n) = A(n - 1) + 5; A(1) = 3
A(n) = A(n - 1) + 6; A(1) = 3
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Problem 3 Got It? What is the 9th term of the arithmetic sequence?

A(9) = 27
A(9) = 9
A(9) = 51
A(9) = 35
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Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

A(n) = A(n - 1) + 3; 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) + 18; A(1) = 23
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Problem 3 Got It? What is the 9th term of the arithmetic sequence?

A(9) = 119
A(9) = 81
A(9) = 151
A(9) = 107
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Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

A(n) = A(n - 1) + 1; A(1) = 7.3
A(n) = A(n - 1) + 1.5; A(1) = 7.3
A(n) = A(n - 1) + 0.5; A(1) = 7.3
A(n) = A(n - 1) + 2.5; A(1) = 7.3
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Problem 3 Got It? What is the 9th term of the arithmetic sequence?

A(9) = 9.3
A(9) = 10.8
A(9) = 11.1
A(9) = 11.3
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Problem 3 Got It? Write a recursive formula for the arithmetic sequence.

A(n) = A(n - 1) + 9; A(1) = 7.3
A(n) = A(n - 1) - 9; A(1) = 7.3
A(n) = A(n - 1) - 3; A(1) = 7.3
A(n) = A(n - 1) + 3; A(1) = 7.3
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Problem 3 Got It? What is the 9th term of the arithmetic sequence?

A(9) = 35
A(9) = 30
A(9) = 25
A(9) = 20
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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?
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Vocabulary: Consider the following arithmetic sequence: 25, 19, 13, 7, ...
Is the common difference 6 or -6? Explain.
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Error Analysis: Describe and correct the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28, ...
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Reasoning: Can you use the explicit formula below to find the nth term of an arithmetic sequence with a first term A(1) and a common difference d. Explain.

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Review Lesson 4-6: Consider the function.
Match each domain element in the left column with its related range element in the right column. Use each domain element only once.
• 5
• -5
• -40
• 12
• 0
• -4
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Review Lesson 4-6: Consider the function.
Match each domain element in the left column with its related range element in the right column. Use each domain element only once.
• 300
• -9
• 0
• 27
• 3
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Review Lesson 2-6: Fill in the blanks.
• A pool fills at a rate of 8 gal/min. This is __?__ gal/h.
• A ball is thrown at a speed of 90 mi/h. This is __?__ ft/sec.
• You buy bottled water in 12-packs that cost \$3 each. If you drink 3 bottles per day, your cost is \$__?__ per week.