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9-12 Algebra 2 Unit 1 Lesson 8

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 Geometry •Algebra 2 Extra Support Materials for Algebra 1

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11

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Unit 3
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Unit 5
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Unit 8

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Lesson 6
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Lesson 8
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Unit 1, Lesson 8

The $n^{\text{th}}$ Term

Algebra 2

Practice

Problem 1

A sequence is defined by \(f(0) = \text-20, f(n) = f(n-1) -5\) for \(n \ge1\).

Explain why \(f(1) = \text- 20 - 5\).
Explain why \(f(3) = \text- 20 - 5 - 5 - 5\).
Complete this expression: \(f(10)=\text-20-\underline{\hspace{.5in}}\). Explain your reasoning.

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Problem 2

A sequence is defined by \(f(0) = \text- 4, f(n) = f(n-1) - 2\) for \(n\ge1\). Write a definition for the \(n^{\text{th}}\) term of the sequence.

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Problem 3

ForLesson 7: Representing More Sequences

Here is the recursive definition of a sequence: \(f(1) = 3,f(n) = 2 \boldcdot f(n-1)\) for \(n\ge2\).

Find the first 5 terms of the sequence.
Graph the value of the term as a function of the term number.
Is the sequence arithmetic, geometric, or neither? Explain how you know.

<p>Blank coordinate plane with grid, origin O. Horizontal axis from 0 to 6 by 1’s, labeled “term number”. Vertical axis from 0 to 60 by 5’s, labeled “value”.</p>

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Problem 4

ForLesson 6: Representing Sequences

Here is a graph of sequence \(M\). Use function notation to define \(M\) recursively.

<p>Graph of a sequence M.</p>

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Problem 5

ForLesson 5: Sequences Are Functions

Write the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither.

\(a(1) = 5, a(n) = a(n-1) + 3\) for \(n\ge2\)
\(b(1) = 1, b(n) = 3 \boldcdot b(n-1)\) for \(n\ge2\)
\(c(1) = 3, c(n) = \text-c(n-1) + 1\) for \(n\ge2\)
\(d(1) = 5, d(n) = d(n-1) + n\) for \(n\ge2\)

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Problem 6

ForLesson 7: Representing More Sequences

Here is the graph of a sequence:

Is this sequence arithmetic or geometric? Explain how you know.
List at least the first five terms of the sequence.
Write a recursive definition of the sequence.

<p>Graph of sequence on coordinate plane.</p>

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Lesson 8 Resources

Student Materials