Finding a Pattern

Date: 11/11/2001 at 17:16:41
From: Ray White
Subject: Number patterns

My daughter received this in a homework assignment, and I don't 
believe there is enough specific information to logically give the 
next four numbers in the sequence: 2, 8, 7, 28.

Date: 11/12/2001 at 14:41:24
From: Doctor Peterson
Subject: Re: Number patterns

Hi, Ray.

I agree, there really is not enough information here. I can guess what 
they probably want, however; most likely they have had other examples 
where they alternated two simple operations to get successive terms, 
and you are expected to assume that this pattern is similar. 

If so, then we are first multiplying by 4 (2*4 = 8), then subtracting 
1 (8-1 = 7), then multiplying by 4 again (7*4 = 28), so you would 
continue in the same way: 27, 108, 107, 428. 

But another perfectly valid pattern would be "for odd terms, add 5 
each time; for even terms, add 20." That would give 12, 48, 17, 68.

If a problem merely says "give the next four numbers" or "find the 
pattern in this sequence," there are infinitely many possible answers, 
since the word "pattern" has no precise definition; it's really a 
matter of guessing what pattern they had in mind, which is not math 
but psychology or ESP. To make this a valid problem, they should say 
something at least as clear as "This sequence was formed by a pattern 
similar to those you saw in this chapter. Make a reasonable guess as 
to what the pattern is, and show how it continues." Or, I suppose, 
they could say "Find a pattern in this sequence, explain how it works, 
and use that pattern to predict the next four numbers. There may be 
more than one correct answer." 

But to imply that students can determine _the_ correct answer by 
looking at four numbers is a misleading lesson in what math is all 
about. It's not a guessing game.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   

Date: 11/13/2001 at 18:54:46
From: Ray White
Subject: Re: number patterns

Very well done, thanks.