# I discovered a formula for the nth term of any sequence of numbers

CompuChip
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In mathematics? There is no wrong answer.

In an IQ test? It's to test whether you can identify patterns so there is a right answer.

I was asked to take such an "IQ test" as part of a job application procedure recently. I more or less openly told them what I thought of these tests, both on how they claim to measure your intelligence as well as how they claim that 3 out of 4 answers are wrong.

Didn't get the job :)

jbunniii
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Gold Member

I was asked to take such an "IQ test" as part of a job application procedure recently. I more or less openly told them what I thought of these tests, both on how they claim to measure your intelligence as well as how they claim that 3 out of 4 answers are wrong.

Didn't get the job :)
Next time I interview someone I should start by asking them to supply the next number in this pattern: ##3, 1, 4, 1, 5, \ldots##. If they answer ##1## then they're robots and I don't want to work with them, so I can dismiss them immediately before we waste any more of each other's time. If they answer ##9## then they're thinking mathematically and we can move on to question 2. ("Prove the Banach-Tarski paradox.")

Next time I interview someone I should start by asking them to supply the next number in this pattern: ##3, 1, 4, 1, 5, \ldots##. If they answer ##1## then they're robots and I don't want to work with them, so I can dismiss them immediately before we waste any more of each other's time. If they answer ##9## then they're thinking mathematically and we can move on to question 2. ("Prove the Banach-Tarski paradox.")

What if they answer 10 and say that they prefer to work in base 9?

jbunniii
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Gold Member

What if they answer 10 and say that they prefer to work in base 9?
Then they can have my boss's job.

CompuChip
Homework Helper

Next time I interview someone I should start by asking them to supply the next number in this pattern: ##3, 1, 4, 1, 5, \ldots##. If they answer ##1## then they're robots and I don't want to work with them, so I can dismiss them immediately before we waste any more of each other's time. If they answer ##9## then they're thinking mathematically and we can move on to question 2. ("Prove the Banach-Tarski paradox.")

Haha, that one's really nice! You're probably right, it wouldn't even have occurred to me to continue with 1 (followed by 6, 1, 7, ...) before you mentioned that.

If you carefully read the original post, you would see that there is no intrinsic flaw in his claim. He is not trying to create a nonsense formula for the nth term in a sequence given a list of the first k terms.

Instead he has a finite sequence u_1, ...., u_n. Given those numbers, he finds an explicit polynomial P(n) such that P(i)=u_i. There is no infinite sequence and it has nothing to do with pattern recognition. It is simply a polynomial interpolation and that is all he is claiming.

If the original post were not clear (which is understandable since the OP is not trained in maths), surely some of the follow up posts would have cleared this up??

finite sequence
No such thing exists.

No such thing exists.

While you're formally correct, it's a bit hairsplitting don't you think? We all know what he meant with it and many people do use this term.

While you're formally correct, it's a bit hairsplitting don't you think? We all know what he meant with it and many people do use this term.

Not at all. I think it's important to use correct terminology; the way things are formally defined in a formal setting.

Not at all. I think it's important to use correct terminology; the way things are formally defined in a formal setting.

It is formal. Many good math books use the terminology "finite sequence". For example: "Mathematical analysis" by Apostol, Definition 2.12.

Or "Real Analysis" by Royden, page 9.

I'm sure I can find many others.

mathwonk
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2020 Award

i don't think so. i have one in mind whose nth term is ??????

Simon Bridge
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If you carefully read the original post, you would see that there is no intrinsic flaw in his claim. He is not trying to create a nonsense formula for the nth term in a sequence given a list of the first k terms.

Instead he has a finite sequence u_1, ...., u_n. Given those numbers, he finds an explicit polynomial P(n) such that P(i)=u_i. There is no infinite sequence and it has nothing to do with pattern recognition. It is simply a polynomial interpolation and that is all he is claiming.
The formula in the first post is not the one OP had in mind - that was posted later. That didn't help matters.
If the original post were not clear (which is understandable since the OP is not trained in maths), surely some of the follow up posts would have cleared this up??
Yet so many people are responding as if the claim is that the formula is predicting the next term in the intended sequence. Like:
i don't think so. i have one in mind whose nth term is ??????
... I don't think OP is actually claiming to be able to predict the next term in mathwonk's sequence ... just to be able to come up with "a" next term given what has gone before and the assumptions (reasoning?) built-in to the formula. The formula would be predictive for a particular kind of sequence.

The wording in post #1 is unclear on this point, and muddied, rather than clarified, by crossed wires in later responses, but I think we are at the point where OP can be encouraged to confirm or deny the interpretation unambiguously.

I submit: further discussion is pointless until that happens.

pwsnafu

The wording in post #1 is unclear on this point, and muddied, rather than clarified, by crossed wires in later responses, but I think we are at the point where OP can be encouraged to confirm or deny the interpretation unambiguously.

I submit: further discussion is pointless until that happens.

He already did so, see the start of post #17. This thread is done, and the original poster said so himself in post #20.

Simon Bridge
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From post #20:
I didn't understand the formulas on the Wikipedia page that you posted here, but now I do. I see that this discussion could have ended a lot sooner.
... not specific.
The confusion still continued though: witness the remaining posts.

I agree the thread is finished with no further input from OP.

Borek
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Locked.