Finding a Rule for a SequenceDate: 07/24/2003 at 13:50:59 From: John Subject: Lots of trouble on this one I have to find the next number and it's a mystery to me. 1, 3, 11, 67, ? Date: 07/25/2003 at 01:34:24 From: Doctor Greenie Subject: Re: Lots of trouble on this one Hi, John - It is impossible to determine what THE next number is in this sequence. Given ANY sequence of numbers, it is possible to develop many different rules which produce that given sequence of numbers - but those many different rules may well produce different "subsequent" numbers. In problems like this, as the number of given numbers increases, it becomes harder and harder to find a rule that fits all the given numbers; but with only the first four numbers given, it is comparatively easy to find a rule that works. Here is one way to find a rule that will find the next number (and subsequent numbers) in the sequence: 1 ==> times 2, plus 1 ==> = 3 3 ==> times 4, minus 1 ==> = 11 11 ==> times 6, plus 1 ==> = 67 And so the next number in the sequence will be 67 ==> times 8, minus 1 ==> = 535 However, as I have noted, this is only one possible answer to the problem. It is quite possible to find completely different rules that generate these first four given numbers but give very different next numbers. I hope this helps. Please write back if you have any further questions about any of this. - Doctor Greenie, The Math Forum http://mathforum.org/dr.math/ |
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