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Categories:

1. Class or Laboratory
2. Courses
3. Tools

Subjects:

1. Precalculus
2. Indexed variables
3. Scatter Plots
4. Graphing
5. Iteration and recursion
6. Sequences and series
7. Fibonacci Sequence
8. Geometry
9. Difference equations

Title: Difference Equations

Book Description: This laboratory focuses on recursively defined sequences. A sequence is like an indexed variable except that it does not necessarily terminate. We will denote a sequence a by the open-ended ordered collection of numbers: ( a(1), a(2), a(3), ..., a(n), ...). The ellipsis at the end means that these numbers go on and on and do not end.
An indexed variable may be thought of as a terminated (or a finite) sequence: ( a(1), a(2), a(3), ..., a(n) ). The infinite nature of sequences betrays the fact that they are always theoretical objects. They must be defined by a rule if they are to continue indefinitely. So they are always abstract models rather than data collected in experiment, because no experiment can provide an infinite number of measurements.
Now sequences are defined by rules, and these rules can have a variety of forms. For example, we might define a sequence by the rule that a(k) = 2*k+1 where k is a nonnegative integer. Then a = ( 1, 3, 5, 7, 9, ...) the positive odd integers. Such a sequence is given by an explicit rule that tells us how to determine the term from the index alone. We'll call such a rule a function rule for the sequence, and we will call the sequence a function sequence. This lab will concentrate on function sequences.

Authors: James White and Dan Kalman

Contained in Precalculus Course.

Suggested Use: Instructions are under the (?) button. The first page of this lab is a Report page and contains the lab assignment with space for students to fill in answers. This has been saved as Notes for that page. To open the report, return to the first page by pressing the Black Rectangle, then select Customize, Notes for this page. To close the notes before leaving the first page, select: Customize, Close Notes

Topics: indexed variables, scatter plots, graphing, recursion, sequences, fibonacci, golden ratio

Number of Pages: 3

Animation: No

Grade Level: