Nth Term of Simple Quadratic Sequences

This applet investigates how to find the nth term of a simple quadratic sequence in the form
an² + b by looking at the differences between succesive terms.

Author and programmer: Ron Barrow

UK Years 7-9, Ages 13-16, KS4, Higher GCSE Mathematics - Number and Algebra

   
           

Instructions below   See also: Sequences  Linear  Harder quadratic  Cubic

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How to Use this Applet

This program starts with a challenge. What is the rule (the nth term) for the sequence of numbers shown?
The sequence is quadratic and has the form: an² + b
By moving the two sliders left and right (by clicking and dragging with the mouse) you can try different rules, to see which one fits the sequence given.

To begin with, the sequences always increase (eg 1,4,9,16..., or 2,7,17,32...). When you feel you understand these types of sequences, then you can make the problem a little harder by also looking at decreasing sequences (eg. 55,50,43,34..... or 4, -4, -16, -32). You do this by unticking the box at the top of the page.
Have a go! You'll soon learn the idea by experimenting for yourself.