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.
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