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**Department of Mathematics Education**

Explorations with some sequences

By Matt Tumlin

1. For
the sequence x(n+1) = 3.2[x(n)][ 1 - x(n)], consider the behavior of the sequence
for various x(0). Using a spreadsheet to display a table and graph for a
sufficient range of n.

To use Excel, Click Here.

Change the value of x(0) in the red cell to explore
different behaviors.

Try positive and negative values. Try values in between 0 and 1.

What happens when x(0) = 0.6875

2. Investigate this sequence for a range of x(0).

x(n+1) = 3.83[x(n)][ 1 - x(n)]

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Change the value of x(0) in the red cell to explore
different behaviors.

Try positive and negative values. Try values in between 0 and 1.

What happens when x(0) = 0.738903394

3. For 0
< A < 2 examine x(n+1) = 1 - A [x(n)]2 for -1 < x(0) < 1

To use Excel, Click Here.

Change the value of A in the red cell and x(0) in the
yellow cell to explore different behaviors.

Try positive and negative values. Try values in between 0 and 1.