Sequences - method of finite differences

Given a sequence, the method of finite differences can be used to try to find a polynomial function that either fits or approximately fits the data. This method involves the use of Newton's forward difference formula.

See the notes for details.

Finding a polynomial function can be viewed as fitting a curve to a set of points.

This java applet shows the points, finds the function and draws the graph.

Consider each problem in Sequences - investigations.

Use the method of finite differences to find a formula for the n-th term of each sequence.

Consider the number of regions of a circle created by drawing all possible diagonals.

Draw the next two diagrams and count the number of regions.

Assuming the polynomial model is appropriate, find a formula for the number of regions on the diagram with n points on the circumference of the circle.