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9-12 Algebra 2 Unit 1 Lesson 7

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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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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 1, Lesson 7

Representing More Sequences

Algebra 2

Practice

Problem 1

Here is the recursive definition of a sequence: \(f(1) = 10, f(n) = f(n-1) - 1.5\) for \(n\ge2\).

Is this sequence arithmetic, geometric, or neither?
List at least the first five terms of the sequence.
Graph the value of the term \(f(n)\) as a function of the term number \(n\) for at least the first five terms of the sequence.

Problem 2

An arithmetic sequence \(k\) starts 12, 6, . . .

Write a recursive definition for this sequence.
Graph at least the first five terms of the sequence.

Problem 3

ForLesson 6: Representing Sequences

An arithmetic sequence \(a\) begins 11, 7, . . .

Write a recursive definition for this sequence, using function notation.
Sketch a graph of the first 5 terms of \(a\).
Explain how to use the recursive definition to find \(a(100)\). (Don't actually determine the value.)

Problem 4

ForLesson 6: Representing Sequences

A geometric sequence \(g\) starts 80, 40, . . .

Write a recursive definition for this sequence, using function notation.
Use your definition to make a table of values for \(g(n)\) for the first 6 terms.
Explain how to use the recursive definition to find \(g(100)\). (Don't actually determine the value.)

Problem 5

ForLesson 5: Sequences Are Functions

Match each recursive definition with one of the sequences.

\(h(1)=1, h(n)=2 \boldcdot h(n-1) + 1\) for \(n\ge2\)
\(p(1) = 1, p(n) = 2 \boldcdot p(n-1)\) for \(n\ge2\)
\(a(1) = 80, a(n) = \frac 1 2 \boldcdot a(n-1)\) for \(n\ge2\)

80, 40, 20, 10, 5
1, 2, 4, 8, 16
1, 3, 7, 15, 31

Problem 6

ForLesson 3: Different Types of Sequences

For each sequence, decide whether it could be arithmetic, geometric, or neither.

25, 5, 1, . . .
25, 19, 13, . . .
4, 9, 16, . . .
50, 60, 70, . . .
\(\frac{1}{2},\) 3, 18, . . .

For each sequence that is neither arithmetic nor geometric, how can you change a single number to make it an arithmetic sequence? A geometric sequence?