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 tools


Instructions below    Waldomaths video    Worksheet on this topic in .pdf form    See also: Linear sequences    Simple quadratic sequences    Harder quadratic sequences

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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".