How to Find Patterns of Sequences
Date: 7/16/96 at 11:56:36 From: Anonymous Subject: Find Pattern of Sequence Hi, Could you help me with the following number sequences: 2,3,1,2,8,9 and 6,10,15,23,31,41 Is there a method that you use to recognize and solve the sequence? Please explain how to solve the above. Thank you very much. P.S. Is there software available to help with this type of problem?
Date: 7/16/96 at 17:40:38 From: Doctor Anthony Subject: Re: Find Pattern of Sequence The short answer is that there is no unique rule to generate this sequence of numbers. I could construct a polynomial of degree 7 to give you the numbers you list, but there can be any number of rules that would give the same set of numbers. A trivial example is 2,4,6 which could be the start of an AP with common difference 2, or the start of a Fibonacci series with the third term the sum of the two previous terms. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 7/16/96 at 11:56:36 From: Anonymous Subject: Re: Find Pattern of Sequence I appreciate your reply, but still do not understand. I think the answer to the first sequence is 5 as the next number, but am not sure. I have no idea how to work the second problem. Can you help me with both?
Date: 7/22/96 at 15:57:35 From: Doctor Ceeks Subject: Re: Sequence/Series Hi, I agree very much with Doctor Anthony's response. Any finite set of numbers can be continued in countless ways to form a sequence. In your problems, the hope is to find a sequence which is as simple to understand as possible. However, it is sometimes hard to know what is simplest. In any case, many sequences have appeared in natural ways in the course of mathematical research, and many of these sequences are recorded in "Handbook of Integer Sequences" by NJA Sloane. Dr. Sloane also wrote a computer program which will try to find sequences to which your sequences belong. To use this program follow these steps: Send e-mail to "firstname.lastname@example.org" with the message: lookup 2 3 1 2 8 9 In a little bit, you will get e-mail from the program with any sequences it finds and bibliographic references to where the sequences found appear in the mathematical literature. Have fun! -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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