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What are the basic/advanced strategies used to find the next number in series.

I know the simple ones such as addition, multiplication etc. But recently I came into a question that goes on something like 812, 819, 823, 835, 834, 851(Don't try to solve this, I changed some numbers and there is no sequence). This is to illustrate that the sequence goes up and goes down at 835 then goes back up. What strategies can you use to solve it?

These questions are for an aptitude test so you have about 60-90 secs to solve each question.

P.S. I can't really post the question that was asked as I might be disqualified from the job process if I post it.

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    "What are the basic/advanced strategies used to find the next number in series.?" - in practice, one usually checks the [OEIS](http://oeis.org/) first.2011-10-21
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    It doesn't find the sequence in OEIS. I have about 5 of these sequences that increases, decreases and increases again. There is no sequence in the table on the website.2011-10-21
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    Without some restriction on what the formula must look like, this problem isn't even well posed: there are infinitely many formulas that generate any given finite sequence (the Lagrange interpolating polynomial of that sequence, for instance) and a lot of times the "right" answer to such puzzles has little if anything to do with math proper (such as the famous 1, 11, 21, 1211, 111221, etc sequence).2011-10-21
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    As a simple example of what user7530 is talking about, what's the next number in this sequence (2, 4, 3), given that the fourth number stands in relation to the third as the second does to the first? Well, one could make a case for 5, since (2+2)=4, and (3+2)=5. One could also make a case for 6, since (2*2)=4, and (3*2)=6. One could also make a case for 9, since (2^2)=4, and (3^2)=9.2011-10-21
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    @Doug: what is the continuation of 4,2,4 ? It's 1. Why? Because when you were asked this question, you've been in a test for getting accepted in a course for becoming a trainer of soccer ... ;-)2011-10-21
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    i dont think OEIS is an option at all because the kind of exam he is talking about would a paper pencil exam (no comp usage at all)2011-10-22
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    @GottfriedHelms I don't follow, because I don't know soccer. I'd guess 4 position players of one type, 2 of another, 4 of another, and 1 goalkeeper. Most team sports have their own sequences when you think about it.2011-10-23
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    @Doug: yes, that's one of the current favorite team-organizations. I just wanted to give an admittedly bizarre example, where sequences are completely non-arithmetical and refer only to (in a test for application of a job) expected special knowledge and mental association. A soccer-trainer *should* immediately *associate* a team-organization, otherwise - "...where does he have his mind?"2011-10-23
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    I usually avoid these questions...2011-12-05

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