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« A Question for the Anti-War Crowd | Main | Rwandan Mischief in the Congo »

December 02, 2004

Comments

Frank McGahon

Well, I'm guessing 121 but you're probably going to tell me that there is another possible sequence in addition to +10,+12,+14,+16,+18..+20?

Julian Elson

I guessed what Frank guessed too.

I'm going to meta-guess (guess about my guess) that such an obvious answer is wrong.

Preston

I think the answer is that without an explicitly stated relationship between the numbers in the sequence, the final number in the set cannot truly be extrapolated i.e. an infinite number of values can fulfill the unstated sequential relationship. :)

captainblak

this is not a series..it's a sequence.

Abiola Lapite

I'm going to hold out for a while on giving a definitive answer, as I have a feeling others will have something to say over the next few hours, but I will respond to the following:
this is not a series..it's a sequence.Actually, it's both; "series" and "sequence" are synonyms.

captainblak

I thought there was a distinction when the terms are used in Mathematics as it says in your link:
----
Mathematics. The sum of a sequentially ordered finite or infinite set of terms.
----

I only took two courses in Math in college so I am probably wrong.

Abiola Lapite

"Mathematics. The sum of a sequentially ordered finite or infinite set of terms."

From the link I provided comes the following:
These nouns denote a number of things placed or occurring one after the other. Series refers to like, related, or identical things arranged or occurring in order: a series of days; a series of facts.It would seem rather odd to think of "a series of day" or "facts" as a sum, wouldn't it? In point of fact, the standard expression used in analysis is to speak of the "sum of a series", indicating clearly enough that one distinguishes the sum from the terms which constitute the series.

captainblak

Well, at first I thought 121 but then as was said, that was too obvious.

Then I remembered the professor making the distinction between what a "series" and a "sequence" was. But I am not the Math authority here.

captainblak

I've cheated and looked up from here...
http://www.sparknotes.com/math/precalc/sequencesandseries/summary.html
" A sequence is a special kind of function whose domain is the positive integers. The range of a sequence is the collection of terms that make up the sequence. Just as the word sequence implies, the order of the terms in a sequence is important."

and
"When the terms of a sequence are summed, the result is called a series."

Abiola Lapite

"When the terms of a sequence are summed, the result is called a series."

I'm supposed to take the word of some Cheathouse-type thing for lazy students over something I know from doing analysis for years why exactly? This is frankly a ridiculous argument, and you're utterly and completely wrong. I'd be grateful if you could spare me the attempts to show why your wrongheaded linguistic pettifoggery is actually justified, as not only is it a futile exercise, but it is also a complete distraction from what the point of this post was.

captainblak

Naturally I don't think the point of this was the distinction between "series" and "sequence". But since you are the one schooled in Mathematics and are a strident advocate of its precision, one would expect that the distinction would have caught your eye (if indeed the distinction is important).
I answered the question before you gave me the dictionary link and before I checked the website, which you don't agree with.
But it is not just that site that emphasises the difference, here's mathworld:

http://mathworld.wolfram.com/Series.html
"A series is an infinite ordered set of terms combined together by the addition operator"

http://mathworld.wolfram.com/Sequence.html
"A sequence is an ordered set of mathematical objects."

Temporary

Lets assume the obvious answer of 121 is false.

There are other useful things one mnay observe about the sequence. All the numbers are prime.

I suppose the answer may lie in the following expanded sequence?

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113

Temporary

103 looks like a good candidate.

Dan Phillips

[Deleted]

[I DID specifically say "no cheating", didn't I? - A.L.]

Temporary

The answer definitely involves a prime.

Temporary

The answer definitely involves a prime.

@DP - I see. Now you've gone and spoiled it.

Dan Phillips

(I'm sorry. All the yelling upset me. No one needed to click on the links though.)

I agree that those sequence questions are dubious considered individually. What they are looking for is the "simplest" solution--but that is subjective. A clever person might see an interesting solution and miss the "simplest" one. But is it likely that that would occur over *many* questions?

Dan Phillips

(Oh, and I missed that this was supposed to be a game. I guess I'm pretty autistic. And it seems I can't read either. My apologies.)

Factory

Hmm, OTOH is that like asking what is the next after 0,1,2,?, it could be of two answers 3 or 4. One is an arithmetic series, the other not.
Then again it is not a good question for a general intelligence test if the right answer depends on mathematical jargon which would not be obvious to the casual reader.

Mugizi  Rwebangira

OK, I didn't look.

121 is the obvious answer, but its so obvious I know it has to be wrong.

Knowing you, its probably something to do with prime numbers and modular arithmetic or somesuch.

Oh wait, I just realized all these numbers are prime.

They are the 11th, 13th, 16th, 19thth, 23rd and 26th primes.

It seems the next one should be the 29th prime.

It still seems wrong but I'll go with 109.

Abiola Lapite

"Naturally I don't think the point of this was the distinction between "series" and "sequence". But since you are the one schooled in Mathematics and are a strident advocate of its precision, one would expect that the distinction would have caught your eye (if indeed the distinction is important)."

I'll be blunt; this is an irrelevant threadjack, and despite the fact that I'd asked you to let it go, you still went on ahead. I don't appreciate in the least your insistence on derailing a conversation I'd hoped would be about more substantive matters.

kenji

This is an excellent post that shows why the argument that all standardized exams are rife with cultural biases should be taken far more seriously than it usually is. It is scary how easy it is to take apart a typical SAT, LSAT, etc., by showing the implicit assumptions embedded in the questions. This is why one's cultural capital determines to a large extent one's potential to succeed in the world.

Alon Levy

Well, every sequence of n+1 numbers defines a unique polynomial of degree n, so given a sequence of n numbers you can have any number as the next term and still maintain a polynomial series.

On the other hand, some relationships are more obvious than others, or else private key cryptanalysis wouldn't exist. The Arab way of noticing certain patterns had no problems in Europe, so I don't think that finding out the next term is very culture-dependent.

Kenji

"The Arab way of noticing certain patterns had no problems in Europe, so I don't think that finding out the next term is very culture-dependent."

Or is it that the cultural similarities, in this case, made the sharing of certain patterns possible?

Abiola Lapite

"On the other hand, some relationships are more obvious than others, or else private key cryptanalysis wouldn't exist."

If these tests were asking one to fill in missing letters in known English words, or to correct mistakes in grammar, this point would be more on target. The thing is, these "culture-free" tests claim to avoid relying on such material in order to minimize the importance of a shared cultural background.

"Or is it that the cultural similarities, in this case, made the sharing of certain patterns possible?"

A better way of looking at things would be to say that the Europeans learned how to think about such things from the Arabs - the very word "algorithm" is Arabic in origin. If it were true that all cultures had exactly the same systems of categorizing things, I fail to see why it is that even languages (e.g. West-Germanic) within the same family often fail to share something as straightforward as a common number-base.

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