Figuring out the next term in a sequence

Jomo

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I have a question about the attitude of the forum members when it comes to figuring out the the next term in a sequence.
1st, I agree that these pattern questions have an infinite number of answers and I am not trying to argue that.
Now part of math is about recognizing patterns. Does anyone one disagree with that?
I guess I agree that we should say that there are infinite number of answers and explain why. But why not help the student see that pattern that most probably (with p=1 !) the author wants?
I did exremely well with integration as a student because I easily saw which pattern the integral matched up with of the ones I learned. Possibly I was better at this because I learned to recognize patterns before?
I suspect for you researcher out there, that recognizing pattern got you some very nice results.
 

ksdhart2

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I agree with you. I also fell victim to the same kind of disagreement from a peer on another math forum and it left a sour taste in my mouth. I really only dislike the find the next number problems when they're just gonzo off-the-wall solutions that practically require you to be a mind reader to figure out the "right" answer. If, for example, a student was given the sequence {1, 3, 5, 7, 9, 11} and asked to find the next number, I would hint them towards noticing the sequence is all the odd numbers. While it's technically true that there are infinitely many other sequences that fit that bill, why complicate things when we don't have to?
 

HallsofIvy

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I would agree if the problem were to find the most *reasonable* next number.
 

Subhotosh Khan

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I would agree if the problem were to find the most *reasonable* next number.
find the most *reasonable* next number of:

1, 2, 4, 8, 16 ........
 

Dr.Peterson

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I agree fully with the approach of simply pointing out that the problem is really asking for what seems likely to be the intended pattern, but then suggesting what to look for (though sometimes it is difficult to give a good hint without giving the whole thing away, especially for the trick questions like "Z, O, T, T, F, F, ..."). I would also consider it very important to accept alternative answers as long as they are logical.

The example SK gives is a classic: 32 is the most reasonable answer if you have been learning about geometric sequences, while 31 is the correct answer if you are thinking about dividing a circle by straight lines (among other things). I suppose even in the "obvious" cases like 1, 3, 5, 7, such alternatives may arise. It's largely context that determines what (if anything) is reasonable.

The key to deciding whether to start with the quibbles or with a friendly hint ought to be knowledge of the asker's age and background; unfortunately on this site we usually don't know anything about that, and have to guess from the wording of the question.
 

Jomo

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topsquark

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Okay, you just lost me. How could the pattern be 31?

-Dan
 

Dr.Peterson

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Okay, you just lost me. How could the pattern be 31?

-Dan
See the link in my post #5 on the number 31.

Then repeat the search there, excluding 31, to see other possible answers, such as 30.
 

topsquark

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See the link in my post #5 on the number 31.

Then repeat the search there, excluding 31, to see other possible answers, such as 30.
Gah! I need to take a nap....

Thanks!

-Dan
 
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