Number sequence IQ question: What is the next term in this sequence?

[Phenomenal]

So what would the next term after 150 be Phenomenal. Would it follow the "rule" or not follow the rule? It's not such a good rule if it's only sometimes followed.

The point is you're only asked for the NEXT number. It doesn't ask you to work out the next several.. Excuse my use of the term rule, you're correct. What I am implying is that this is the only 'pattern' that really applies and thus 150 makes perfect sense.

This is one question in an IQ test as already said, it's not expected that the situation is overanalysed using the previous calculations that have already been done so far in this thread.

 

[The Chaz]

The point is you're only asked for the NEXT number. It doesn't ask you to work out the next several.. Excuse my use of the term rule, you're correct. What I am implying is that this is the only 'pattern' that really applies and thus 150 makes perfect sense.

This is one question in an IQ test as already said, it's not expected that the situation is overanalysed using the previous calculations that have already been done so far in this thread.

Uart has failed to justify these extensive calculations in the context of an IQ test and - more generally - hasn't addressed any of my three points from 9:46am a few weeks back. (can't see the date or the post number on my iPhone)...
I'll let you omit your response to my #1 ;)

 

[Dickfore]

I can only find this justification for 150. If we write down the differences:

<br /> \begin{array}{cc}<br /> 3 &amp; \\<br /> &amp; 5 \\<br /> 8 &amp; \\ <br /> &amp; 10 \\<br /> 18 &amp; \\<br /> &amp; \mathbf{12} \\<br /> 30 &amp; \\<br /> &amp; 40 \\<br /> 70 &amp; \\<br /> \end{array}<br />

I see that the twelve "sticks out" from the sequence. It would be much nicer if it were a twenty. And, indeed, in many languages twelve and twenty are similar words and small children often make the mistake of confusing them (in English, a similar situation arises from the -teen's and the -ty's).

If it were 20 instead of 12, then the first differences would form a geometric progression with a quotient 2 and the next term in this sequence (the first differences) would be 80.

But, the next term in the original sequence is equal to the sum of the previous term and the last first difference, namely:

70 + 80 = 150

 

[The Chaz]

As to #3 from a previous post of mine...
1,2,4,8,16,31 is justified as the number of pieces in a circle, when segments are drawn between 1,2,3,4,5, and 6 points on its circumference.

"Number Freak" by Niederman gives explanations for how "30" and "33" could also complete the sequence
1,2,4,8,16__

30: the number of divisors in (6!).
33: the number of ways in which the first player gets killed in a five-player Russian Roulette game using a gun having n chambers, where the number of bullets can equal anything from 1 to n, with no rotations of the cylinder allowed.

 

[Chris11]

LOL. The pattern detecting system couldn't even detect the following pattern: 2, 4, 8, 16,..., 2^n

 

[Noxide]

3, 8, 18 , 30, 70, 150 , 300, 690, 1470, ...dumb question

 

[Dickfore]

3, 8, 18 , 30, 70, 150 , 300, 690, 1470, ...


dumb question

would you mind elaborating how you obtained this continuation of the sequence?

 

[Noxide]

would you mind elaborating how you obtained this continuation of the sequence?

A = 3, 8, 18, 30, 70, 150, 300, ... <=> A = a, b, d, e, f, h, i, ...

a = 3 (arbitrary)
b = 8 (arbitrary)
b-a = c
b + 2c = d
e = 10a
f = 10(b-1)
f-e = g
2g + f = h
10e = i
...

i.e. the sequence is uniquely determined by a given a and b such that sequence a, b, c, ... = A

A = a, b, b+2(b-a), 10a, 10(b-1), 2[10(b-1) - 10a] + 10(b-1), 10(10a), 10[10(b-1)], 2{10[10(b-1)]- 10(10)a}, ...

 

[Dickfore]

A = 3, 8, 18, 30, 70, 150, 300, ... <=> A = a, b, d, e, f, h, i, ...

a = 3 (arbitrary)
b = 8 (arbitrary)
b-a = c
b + 2c = d
e = 10a
f = 10(b-1)
f-e = g
2g + f = h
10e = i
...

i.e. the sequence is uniquely determined by a given a and b such that sequence a, b, c, ... = A

A = a, b, b+2(b-a), 10a, 10(b-1), 2[10(b-1) - 10a] + 10(b-1), 10(10a), 10[10(b-1)], 2{10[10(b-1)]- 10(10)a}, ...

You can combine your definition of c and d, to eliminate the intermediate value c (and g further on):
<br /> d = b + 2c = b + 2(b - a) = 3b - 2a<br />
Other than that, you logic seems like stabbing in the dark to find the given answer 150.

 

[Chris11]

Moral of the Story: IQ tests are meaningless

 

[Noxide]

You can combine your definition of c and d, to eliminate the intermediate value c (and g further on):
<br /> d = b + 2c = b + 2(b - a) = 3b - 2a<br />
Other than that, you logic seems like stabbing in the dark to find the given answer 150.

Of course I can, and I did: A = a, b, b+2(b-a), 10a, 10(b-1), 2[10(b-1) - 10a] + 10(b-1), 10(10a), 10[10(b-1)], 2{10[10(b-1)]- 10(10)a}, ...
A is defined purely in terms of a and b

How is it stabbing in the dark?
The difference between the first two terms is half the difference between the second and third terms. The sequence has units that are triplets...

 

[Dickfore]

Of course I can, and I did: A = a, b, b+2(b-a), 10a, 10(b-1), 2[10(b-1) - 10a] + 10(b-1), 10(10a), 10[10(b-1)], 2{10[10(b-1)]- 10(10)a}, ...
A is defined purely in terms of a and b

How is it stabbing in the dark?
The difference between the first two terms is half the difference between the second and third terms. The sequence has units that are triplets...

What's the logic for 10(b - 1) in the second term of the second triplet, i.e. 70? If you followed any logic from the previous one, you should have written 80.

 

[The Chaz]

What's the logic for 10(b - 1) in the second term of the second triplet, i.e. 70? If you followed any logic from the previous one, you should have written 80.

Maybe this is less a dumb question than a dumb answer...?
That this comes from an IQ test is the only justification for considering the (or a) pattern observed in the first three terms and applying that to the next set of three.

This reminds me of the analogy questions on the old SAT. Something like
fish:water::telephone:_______

 

[Dickfore]

Let us use polynomial inetrpolation:

<br /> \begin{array}{ccccc}<br /> 3&amp; &amp; &amp; &amp; \\<br /> &amp;5&amp; &amp; &amp; \\<br /> 8&amp; &amp;5&amp; &amp; \\<br /> &amp;10&amp; &amp;-3 \\<br /> 18&amp; &amp;2&amp; &amp;19\\<br /> &amp;12&amp; &amp;16&amp; \\<br /> 30&amp; &amp;18&amp; &amp;\mathbf{19}\\<br /> &amp;40&amp; &amp;35&amp; \\<br /> 70&amp; &amp;53&amp; &amp; \\<br /> &amp;93&amp; &amp; &amp; \\<br /> \mathbf{163}&amp; &amp; &amp; &amp; <br /> \end{array}<br />

 

[uart]

Of course I can, and I did: A = a, b, b+2(b-a), 10a, 10(b-1), 2[10(b-1) - 10a] + 10(b-1), 10(10a), 10[10(b-1)], 2{10[10(b-1)]- 10(10)a}, ...
A is defined purely in terms of a and b

How is it stabbing in the dark?
The difference between the first two terms is half the difference between the second and third terms. The sequence has units that are triplets...

That's ok, but the following "triplet" solution is no more (or no less) arbitrary.

3 8 18 : 30 70 2097 : 57 132 7506 :

The third term in each triplet is the product of the previous two terms minus the digit sum (of that product). For example 3*8=24 and 24-2-4 = 18.

The triplets are continued via T_{3n+1} = T_{3n-2} + 27 and T_{3n+2} = T_{3n-1}+62, starting with T1 = 3 and T2 = 8.

 

[Tedjn]

I've got an even better idea. Let's plot the sequence against n, draw a random curve through those points, and then look at the graph! An experimental way to decide it once and for all.

 

[Phenomenal]

Maybe this is less a dumb question than a dumb answer...?
That this comes from an IQ test is the only justification for considering the (or a) pattern observed in the first three terms and applying that to the next set of three.

This reminds me of the analogy questions on the old SAT. Something like
fish:water::telephone:_______

Funny how the logical explanation has yet again been ignored and overlooked by you guys.

I assume you're just trying to worth out a real "pattern" in these numbers now to prove there IS indeed a pattern, correct?

Without logic we are adrift on a sea of rationalizations.

 

[Count Iblis]

http://www.mat.univie.ac.at/~kratt/rate/rate.html

 

[Noxide]

That's ok, but the following "triplet" solution is no more (or no less) arbitrary.

3 8 18 : 30 70 2097 : 57 132 7506 :

The third term in each triplet is the product of the previous two terms minus the digit sum (of that product). For example 3*8=24 and 24-2-4 = 18.

The triplets are continued via T_{3n+1} = T_{3n-2} + 27 and T_{3n+2} = T_{3n-1}+62, starting with T1 = 3 and T2 = 8.

This cannot be the case... You are overlooking an axiom of the sequence. That axiom being the difference between the first two terms of the triplet is half of the difference between the 2nd and third terms of each triplet.

 

[Dickfore]

This cannot be the case... You are overlooking an axiom of the sequence. That axiom being the difference between the first two terms of the triplet is half of the difference between the 2nd and third terms of each triplet.

lolwut? Where was this axiom postulated?

 

[Chris11]

Lol yeah, where has the axiom been postulated? Anyways, you're taking this question far too seriously, and, probably, whatever IQ test you got it from far to seriously as well... IQ tests aren't even supported very well by even those who administer them--except for hi-IQ societies--that arn't scientific. IQ dosen't really tell you much about a person, except for in the extreems, in which case it's unlikly that you're not stupid if you have an IQ of 73, and you're unlikely to be not smart if you have an IQ>125... There's no gurentee. There are people who have IQs above 140 who don't do anything with there lives, lack any significant academic skill, and display no behavior indicitive of intelligence.

 

[shinkyo00]

Not good. You've given a solution to a different problem, or changed the first term in the sequence to make it fit your solution. The first term was supposed to be 3.

hey

oh i must've copied the original series wrong (i did do this at around 4 am)

so possibly a solution to a different problem, but not "changed the first term in the sequence to make it fit"

but you're right, my solution's 100% wrong

 

[shinkyo00]

Lol yeah, where has the axiom been postulated? Anyways, you're taking this question far too seriously, and, probably, whatever IQ test you got it from far to seriously as well... IQ tests aren't even supported very well by even those who administer them--except for hi-IQ societies--that arn't scientific. IQ dosen't really tell you much about a person, except for in the extreems, in which case it's unlikly that you're not stupid if you have an IQ of 73, and you're unlikely to be not smart if you have an IQ>125... There's no gurentee. There are people who have IQs above 140 who don't do anything with there lives, lack any significant academic skill, and display no behavior indicitive of intelligence.

What do you mean they're not "supported very well" by those who administer them?

I.Q. tells us exactly the "I.Q." of a person and depending on the test administered, a rating in the qualities that the test's supposed to measure, e.g. cognitive reflex or fluid reasoning, etc. Really though, it's not like we expect it to tell us any more. Otherwise it's like expecting B.M.I. to tell us exactly how well a person will do in a certain sport.

You're absolutely right in stating the fact that some people with I.Q. above 140 who don't achieve anything. However, that's achievement and not "intelligence" as meant by the tests.

It appears in your post you're just ripping on I.Q. testing... =/

 

[asdfghjklqqww]

the next number is 176
why?
just a guess really...

 

[Chris11]

What do you mean they're not "supported very well" by those who administer them?

I.Q. tells us exactly the "I.Q." of a person and depending on the test administered, a rating in the qualities that the test's supposed to measure, e.g. cognitive reflex or fluid reasoning, etc. Really though, it's not like we expect it to tell us any more. Otherwise it's like expecting B.M.I. to tell us exactly how well a person will do in a certain sport.

You're absolutely right in stating the fact that some people with I.Q. above 140 who don't achieve anything. However, that's achievement and not "intelligence" as meant by the tests.

It appears in your post you're just ripping on I.Q. testing... =/

You're right. It does tell you what your IQ is. However, my problem with IQ is that IQ has become synomonous with intelligence in popular society. Further, their precision can be called into question: a person under inhibitions can easily score SDs under their 'actual' IQ level. Also, it has been shown in longitudial studies that people's IQs can vary by as much as 2 SDs, given valid testing. No one has an IQ until it is measured, and it's important to keep in mind that these scores are not, as many people believe, inherent properties of the individual being tested.

Also, BMI is actually a more valid measure as it does not rely upon a person's performance on administering the test or writing the test being administered, which are both subject to ENORMOUS fluctuations over the course of as little time as a week.

By 'not supported very well by people who administer them,' I mean that the majority of praticing psychiatrists have little to no faith in IQ testing and its ability to provide a valid measure of intelligence.

 

[shinkyo00]

You're right. It does tell you what your IQ is. However, my problem with IQ is that IQ has become synomonous with intelligence in popular society.

Then I think your problem should be with those who misunderstand it and not with the subject itself! :)

Further, their precision can be called into question: a person under inhibitions can easily score SDs under their 'actual' IQ level.

If someone doesn't use the instrument as intended and ends up with an inaccurate result, it's not the instrument's fault! So a very drunk physicist measures and reports a length incorrectly - do we throw out the ruler or discipline the physicist?

Also, it has been shown in longitudial studies that people's IQs can vary by as much as 2 SDs, given valid testing.

Fine, but so what? If we measure a beanstalk today and the measurement differs a week later, do we conclude that the ruler is broken? In any case, no one here has been insisting that I.Q. is fixed.

No one has an IQ until it is measured, and it's important to keep in mind that these scores are not, as many people believe, inherent properties of the individual being tested.

Again, no one here has been insisting that I.Q. is fixed.

Also, BMI is actually a more valid measure as it does not rely upon a person's performance on administering the test or writing the test being administered, which are both subject to ENORMOUS fluctuations over the course of as little time as a week.

You mean reliable, possibly more accurate.

By 'not supported very well by people who administer them,' I mean that the majority of praticing psychiatrists have little to no faith in IQ testing and its ability to provide a valid measure of intelligence.

Well, if it's written out in full technical detail, every person who's studied psychometrics should understand that "intelligence" in the context of I.Q. testing has a very precise meaning that is not the same as what is meant when used in the mainstream... so what faith is there to be had? If the practitioner firmly states that I.Q. isn't what intelligence is entirely about, then strictly speaking, it's redundant given the understanding of psychometrics. If the practitioner firmly states that I.Q. is exactly what intelligence is and that the converse is also true, then that's their own opinion and it has no bearing on what psychometrics is about and whether psychometric tools are valid or not.

Anyway, it still sounds like you have a problem with the public's misunderstanding and not with I.Q. testing itself.

 

[alice22]

Lol yeah, where has the axiom been postulated? Anyways, you're taking this question far too seriously, and, probably, whatever IQ test you got it from far to seriously as well... IQ tests aren't even supported very well by even those who administer them--except for hi-IQ societies--that arn't scientific. IQ dosen't really tell you much about a person, except for in the extreems, in which case it's unlikly that you're not stupid if you have an IQ of 73, and you're unlikely to be not smart if you have an IQ>125... There's no gurentee. There are people who have IQs above 140 who don't do anything with there lives, lack any significant academic skill, and display no behavior indicitive of intelligence.

"There are people who have IQs above 140 who don't do anything with there lives, lack any significant academic skill, and display no behavior indicitive of intelligence"

Really?

That's a rather sweeping statement!

They are certainly good at getting the right answer in IQ tests, which requires some kind of logical ability assuming the test is a good one.
"don't do anything with their lives"? What are they supposed to do? Run a bank and bankrupt it? Or start a world war?
Maths is academic, hard to see how someone with such a high IQ would be bad at maths.
I doubt anyone with a low IQ would be too good at maths, I would question the maths test or the IQ test if they were.

Maths is pretty precise, the answer is usually not a matter of opinion.

Anyway I don't think there has a been a good answer provided yet, I suspect the question
is a bad or erroneous one, but I would think someone would be able to make a plausible answer that was not massively complicated.

However it is quite a long sequence and each number in it adds another level of complexity.

What it does show I think is that number sequences questions are rather poor IQ questions because the number of possible answers is only limited by your imagination.

Maybe there should be a reward for the first person to solve it!

 

[shinkyo00]

"There are people who have IQs above 140 who don't do anything with there lives, lack any significant academic skill, and display no behavior indicitive of intelligence"

Really?

That's a rather sweeping statement!

They are certainly good at getting the right answer in IQ tests, which requires some kind of logical ability assuming the test is a good one.
"don't do anything with their lives"? What are they supposed to do? Run a bank and bankrupt it? Or start a world war?
Maths is academic, hard to see how someone with such a high IQ would be bad at maths.
I doubt anyone with a low IQ would be too good at maths, I would question the maths test or the IQ test if they were.

Maths is pretty precise, the answer is usually not a matter of opinion.

Anyway I don't think there has a been a good answer provided yet, I suspect the question
is a bad or erroneous one, but I would think someone would be able to make a plausible answer that was not massively complicated.

However it is quite a long sequence and each number in it adds another level of complexity.

What it does show I think is that number sequences questions are rather poor IQ questions because the number of possible answers is only limited by your imagination.

Maybe there should be a reward for the first person to solve it!

Hi Alice, which sequence hasn't been solved yet? And no, number sequences aren't all poor I.Q. questions.

Anyway, which test did you get this sequence from?

 

[shinkyo00]

Ok solved it. Turns out it's a really beautiful question!

Answer: 126

or not...checked and saw that someone's already posted 126 so I'm guessing 126's not it

btw, has 126 been checked? by the OP, that is

p.s. if 126 turns out to be correct, i'll give a simpler method to derive it, as opposed to the method dickfore gave

 

[Chris11]

"There are people who have IQs above 140 who don't do anything with there lives, lack any significant academic skill, and display no behavior indicitive of intelligence"

Really?

That's a rather sweeping statement!

They are certainly good at getting the right answer in IQ tests, which requires some kind of logical ability assuming the test is a good one.
"don't do anything with their lives"? What are they supposed to do? Run a bank and bankrupt it? Or start a world war?
Maths is academic, hard to see how someone with such a high IQ would be bad at maths.
I doubt anyone with a low IQ would be too good at maths, I would question the maths test or the IQ test if they were.

Maths is pretty precise, the answer is usually not a matter of opinion.

Anyway I don't think there has a been a good answer provided yet, I suspect the question
is a bad or erroneous one, but I would think someone would be able to make a plausible answer that was not massively complicated.

However it is quite a long sequence and each number in it adds another level of complexity.

What it does show I think is that number sequences questions are rather poor IQ questions because the number of possible answers is only limited by your imagination.

Maybe there should be a reward for the first person to solve it!

Dyscalcula. Look it up. Many extreemly smart individuals have existed who have been absolutly dreadful at mathematical reasoning. For instance, one of my philosphy professors.


Also, number sequences are essencial to IQ testing. They are one of the fundamental components of any IQ test.