Nth Term of Cubic Sequences
This applet investigates a method of differences to find the nth term of a cubic sequence - an³ + bn² + cn + d. It demonstrates a systematic method for finding the nth term, to practise it, and to see why it works
Author and programmer: Ron Barrow
UK Years 10-13, KS4, KS5, Higher GCSE Mathematics, AS - Shape and Space, Investigative toolsTweet
How to Use this Applet
This program is essentially a machine for finding the rule or formula for a cubic sequence (S) which has: nth term = an³ + bn² + cn + d
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, c and d, which are all integers. If the box "increasing 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 cubic). 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 top. This applet uses a "method of differences".