Math CentralQuandaries & Queries


Question from Shawn, a parent:

I'm a parent and don't know how to help my 6th grader solve for this problem.

Name the next tree terms in this sequence and tell the rule used to find each:



This is a very strange and appropriate sequence to give to a 6th grader. There is an on-line encyclopedia of integer sequences where you can enter a few terms of a sequence and a search is performed in their database to see if they know the sequence. Entry of your sequence yields

a(n) = a(n-3)3 + a(n-2)2 + a(n-1); a(1) = -1, a(2) = 0, a(3) = 1

This says that you start with the three terms -1, 0, 1. To find the fourth term let n = 4 and then

a(4) = a(1)3 + a(2)2 + a(3) = (-1)3 + 02 + 1 = 0

and for the 5the term

a(5) = a(2)3 + a(3)2 + a(4) = (0)3 + 12 + 0 = 1

and so on.


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