# Nth Term of Quadratic Sequences

This applet investigates the method of differences to find the `n`th term of an integer quadratic sequence - `an² + bn + c`. It demonstrates a systematic method for finding the `n`th term, to practise it, and to see why it works

UK Years 10-13, KS4, KS5, Higher GCSE Mathematics, AS - Shape and Space, Investigative tools

Instructions below See also: Linear sequences Simple quadratic sequences Cubic sequences PRINT

## How to Use this Applet

This program is essentially a machine for finding the rule or formula for a quadratic sequence (S), which has `n`th term = **a**`n`² + **b**`n` + **c**, where `n` is the term or sequence number (1, 2, 3, 4, 5, etc.). A new problem is generated randomly by clicking the "new problem" button, and for each new problem you are trying to find the values of **a**, **b** and **c**, which are all integers. If the box "increasing sequences only" is ticked then **a** is always positive. If not then **a** can be positive or negative (but never zero, as this would mean that the sequence is not quadratic!). Clicking the "reset" button takes you back to the beginning of the current sequence. You can show or hide the graph or the working by using the boxes at the bottom. This applet uses what is known as a "method of differences". Play around!