# Iterating a difference equation

This applet iterates a difference equation (also known as recurrence relation) and displays the resulting sequence both graphically and numerically.

Enter a rule for in the text box, and select an initial condition by dragging or typing a value. Drag the slider at the bottom to see more or less terms of the sequence.

The numerical values of the sequence, produced by iteration, are shown in the spreadsheet to the right.

Some interesting difference equations to try:

• $x_{n+1} = (1/2)*x_n+2$
• $x_{n+1} = (-9/10)*x_n+1$
• $x_{n+1} = 3.5**x_n*(1-x_n)$

Other resources:

Geogebratube page for this applet