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

[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.

 

[Chris11]

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



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?



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.



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



You mean reliable, possibly more accurate.



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.

Yes! You are right. However, it is this misunderstanding, that people don't realize is such, that IQ tests are known for. Yes it does have a bearing upon whether or not pscycometric tools are valid in pratice. This is a legitmate appeal to authority.

 

[shinkyo00]

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.

Wrong. Raven's Progressive Matrices, Raven's Advanced Progressive Matrices are just 2 examples that don't use number sequences.

 

[shinkyo00]

Yes! You are right. However, it is this misunderstanding, that people don't realize is such, that IQ tests are known for. Yes it does have a bearing upon whether or not pscycometric tools are valid in pratice. This is a legitmate appeal to authority.

What are you talking about? An uninvolved (in the sense of not being involved in the development or evaluation thereof) personal opinion has no bearing on the validity of something that is the product of intensive research, screening and very strict peer review among other things.

It's not a legitimate appeal to authority at all.

So what if that's what I.Q. tests are known for in the public's mind? The point here is that the people are responsible for their understanding of something. If they misunderstand, that is no cause for holding anything against the subject they misunderstood.

Suppose a very incompetent judge reviews the case of an underage pregnancy. Suppose there is a law that punishes such pregnancies. Now, let's suppose the girl was raped. So does the judge here lay down punishment, or decide that the girl is an innocent victim?

 

[Chris11]

Wrong. Raven's Progressive Matrices, Raven's Advanced Progressive Matrices are just 2 examples that don't use number sequences.

Correct, however those particular tests are very old, and are not general enough to provide an accurate assesment of human intelligence. Did you even look up dyscalculia?

 

[shinkyo00]

Correct, however those particular tests are very old, and are not general enough to provide an accurate assesment of human intelligence.

Doesn't change the fact that they're I.Q. tests! In fact, because you said "any" (implying all), I can refer to Binet's "home-made" (in comparison to today's tests) test way back and you'd still be wrong.

I think you'd have to concede this point.

By the way, what was mentioned (by you) is that number sequences is essential and not that modern tests use them (and so we exclude old ones from the debate), not that we only consider tests that gauge different aspects, etc.

 

[Chris11]

Doesn't change the fact that they're I.Q. tests! In fact, because you said "any" (implying all), I can refer to Binet's "home-made" (in comparison to today's tests) test way back and you'd still be wrong.

I think you'd have to concede this point.

Yes I said any. Oh well. That was a mistake. None of those tests that you have mentioned are even used very often, if at all. The most common IQ test that is used is the WISC or WAIS, which both feature numerical sequence problems. Also, you are not addressing my main argument which is against the 'validity' of IQ testing. You have failed to address the most relevant points that I have raised in our discussion after your first reply to one of my comments. They are 'IQ' tests, but the main point is that they are not generally accepted methods, and are either completely outdated or far too specific to provide any truly scientific measurement.

IQ tests are only useful in identifying learning disiblities and pottential giftedness or mental retardation. And, in the last 2, great or poor performance on an IQ test is not a sufficent or nessacary condition.

Furthermore, whenever a specific intellectual disability is identified via IQ testing, what happens is that the person conducting the assesment adjusts scores to obtain what they feel is a more accurate measure. This means that IQ test, as it was, was not valid. Further, as these adjustments are by no means standardized, this means that their new, adjusted IQ score is also not a scientific measurement.

I was a member of mensa a while ago, and I attended some meetings. At these meetings, those who showed up generally talked and thought about nothing other than IQ testing, and equating intelligence with IQ, they talked about their ascomplishments. Several of those who showed up that day displayed no signs of high intelligence other than that they were members of the organization and that they were good scrable players. In terms of thoughtfullness (in the literal sense), most of them were lacking. In terms of ability, most of them were also lacking as whatever curiousities and natural gifts that they may or may not have possessed were used to obsess over what is essencially a meaningless number.

 

[shinkyo00]

None of those tests that you have mentioned are even used very often, if at all.

That's a moot point. They're still accepted as psychometric instruments. Not very often doesn't mean they're not accepted anymore. Again, there are other tests out there that do not feature number sequences.

Also, you are not addressing my main argument which is against the 'validity' of IQ testing. You have failed to address the most relevant points that I have raised in our discussion after your first reply to one of my comments. They are 'IQ' tests, but the main point is that they are not generally accepted methods, and are either completely outdated or far too specific to provide any truly scientific measurement.

Which main argument exactly did I not address? I made the distinction between a technical definition of intelligence and an everyday usage of the word, which I believe is what you're trying to express but have not. Please refer back to previous posts regarding why your arguments against I.Q. testing in general are not correct.

Not generally accepted methods of what? If they're not generally accepted, please explain why the field of psychometrics still exists, and why this field is still producing results that involve I.Q., and why new revisions of I.Q. tests are still being produced. Please provide a source that substantiates your claim.

Far too specific to provide any truly scientific measurement? Wasn't precision what you were after? In all seriousness, please explain how anything can be so specific that it's not scientific.

IQ tests are only useful in identifying learning disiblities and pottential giftedness or mental retardation.

Tautology.

And, in the last 2, great or poor performance on an IQ test is not a sufficent or nessacary condition.

Wrong. Schools in Asia still used I.Q. tests as a necessary and sufficient condition for admittance to gifted/accelerated programs in the last 10-15 years, that I personally know of.

Furthermore, whenever a specific intellectual disability is identified via IQ testing, what happens is that the person conducting the assesment adjusts scores to obtain what they feel is a more accurate measure. This means that IQ test, as it was, was not valid.

Further, as these adjustments are by no means standardized, this means that their new, adjusted IQ score is also not a scientific measurement.

That just means that specific testing has to be adjusted for. It doesn't mean the entirety of I.Q. testing methodology, psychometrics, research in any way involving I.Q. is invalid. All it means is that other factors, that can't currently be objectively accounted for, have influenced the score and therefore the score itself is compromised.

I was a member of mensa a while ago, and I attended some meetings. At these meetings, those who showed up generally talked and thought about nothing other than IQ testing, and equating intelligence with IQ, they talked about their ascomplishments. Several of those who showed up that day displayed no signs of high intelligence other than that they were members of the organization and that they were good scrable players. In terms of thoughtfullness (in the literal sense), most of them were lacking. In terms of ability, most of them were also lacking as whatever curiousities and natural gifts that they may or may not have possessed were used to obsess over what is essencially a meaningless number.

It is true that many of these organizations have members that are mistaken, misled, etc. It's also true that there is a fascination with I.Q. testing and intelligence. However, if you're going to judge a subject based on unrelated anecdotal evidence, then please, retract all your arguments so far and do more research before you make any more claims.

Essentially, the last paragraph you posted has nothing at all to do with I.Q. testing. So there exists a club for lawyers. Suppose you happen onto them while they're at a club meeting and you overhear them all giving confessions. Suppose this happens again and again. Do you now conclude that all lawyers are brutally honest people and that law degrees are a great thing since they identify those who are honest?

 

[Chris11]

That's a moot point. They're still accepted as psychometric instruments. Not very often doesn't mean they're not accepted anymore. Again, there are other tests out there that do not feature number sequences.
Which main argument exactly did I not address? I made the distinction between a technical definition of intelligence and an everyday usage of the word, which I believe is what you're trying to express but have not. Please refer back to previous posts regarding why your arguments against I.Q. testing in general are not correct.

Not generally accepted methods of what? If they're not generally accepted, please explain why the field of psychometrics still exists, and why this field is still producing results that involve I.Q., and why new revisions of I.Q. tests are still being produced. Please provide a source that substantiates your claim.

Far too specific to provide any truly scientific measurement? Wasn't precision what you were after? In all seriousness, please explain how anything can be so specific that it's not scientific.
Tautology.
Wrong. Schools in Asia still used I.Q. tests as a necessary and sufficient condition for admittance to gifted/accelerated programs in the last 10-15 years, that I personally know of.
That just means that specific testing has to be adjusted for. It doesn't mean the entirety of I.Q. testing methodology, psychometrics, research in any way involving I.Q. is invalid. All it means is that other factors, that can't currently be objectively accounted for, have influenced the score and therefore the score itself is compromised.
It is true that many of these organizations have members that are mistaken, misled, etc. It's also true that there is a fascination with I.Q. testing and intelligence. However, if you're going to judge a subject based on unrelated anecdotal evidence, then please, retract all your arguments so far and do more research before you make any more claims.

Essentially, the last paragraph you posted has nothing at all to do with I.Q. testing. So there exists a club for lawyers. Suppose you happen onto them while they're at a club meeting and you overhear them all giving confessions. Suppose this happens again and again. Do you now conclude that all lawyers are brutally honest people and that law degrees are a great thing since they identify those who are honest?

That was not a tautology

Look. I'm not attempting to discredit the entire field of psychometric. Pschometrics exists because it can provide us with useful measurements in certain situations. When I meant to specific to provide any scientific measurement, what I was saying was that they were to specific to provide any scientific measurement of human intelligence.

I have entirely accepted the distincition that you have made. What I'm arguing against is public misconception, and the obsession that many people have with IQ testing. It is a measure that provides us with some valuable information about an individiual, provided that they are administered correctly.

The antedotal evidence is exactly what was needed to support the claim that I made before: that there are some people with high IQs that aren't truly 'gifted' at anything. The last paragraph had to do with something that I had mentioned earlier that you happened to object to... No I would not think that "all" lawyers were brutly honest people. I wouldn't insert an all quantifier in that circumstance. I would insert a some quantifier... I only claimed that SOME people with high IQs are low in most everything assosiated with organic intelligence, rather than the operationaly defined facsimile.

What you didn't address was the myriad of exceptions to the rule: people who are identified as having dyscalcula, dyslexia, or any other intelectual disability that severly affects their IQ score on an unadjusted test. Further, what you also didn't address, was the correlaries of that assertion. They are significant in number enough to be critical counterexamples.

 

[Chris11]

Then I think your problem should be with those who misunderstand it and not with the subject itself! :)
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?
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.
Again, no one here has been insisting that I.Q. is fixed.
You mean reliable, possibly more accurate.
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.

The bean stock analogy was horrible. IQ is supposed to be a stable measure. It is supposed to measure something truly innate in the individual--something that has virtually no oppurtunity to change.

 

[asdfghjklqqww]

it's funny how this thread started about the solution to a number pattern and is now a bunch of... people complaining about IQ tests!

 

[shinkyo00]

it's funny how this thread started about the solution to a number pattern and is now a bunch of... people complaining about IQ tests!

just him, not me

btw, we have 3, 8, 18, 30, 70

if we add each number to the next one, we end up with:

11, 26, 48, 100

repeating it with this result, we end up with:

37, 74, 148

so, we have each term multiplying by 2 to get the next, which means the next term in this is 296

working backwards, we end up with 126 for the next term in the original sequence

 

[shinkyo00]

That was not a tautology

Look. I'm not attempting to discredit the entire field of psychometric. Pschometrics exists because it can provide us with useful measurements in certain situations. When I meant to specific to provide any scientific measurement, what I was saying was that they were to specific to provide any scientific measurement of human intelligence.

I have entirely accepted the distincition that you have made. What I'm arguing against is public misconception, and the obsession that many people have with IQ testing. It is a measure that provides us with some valuable information about an individiual, provided that they are administered correctly.

The antedotal evidence is exactly what was needed to support the claim that I made before: that there are some people with high IQs that aren't truly 'gifted' at anything. The last paragraph had to do with something that I had mentioned earlier that you happened to object to... No I would not think that "all" lawyers were brutly honest people. I wouldn't insert an all quantifier in that circumstance. I would insert a some quantifier... I only claimed that SOME people with high IQs are low in most everything assosiated with organic intelligence, rather than the operationaly defined facsimile.

What you didn't address was the myriad of exceptions to the rule: people who are identified as having dyscalcula, dyslexia, or any other intelectual disability that severly affects their IQ score on an unadjusted test. Further, what you also didn't address, was the correlaries of that assertion. They are significant in number enough to be critical counterexamples.

It's a statement that's always true because of the definition. Therefore, a tautology. Look man, I go to the trouble of taking each of your points, whether they have any relation to your main argument or not, and replying to them. You're just throwing some anecdotal evidence at me and making some claims based on opinion and assumptions that aren't consistent with the literature. I think I'll give up.

 

[shinkyo00]

The bean stock analogy was horrible. IQ is supposed to be a stable measure. It is supposed to measure something truly innate in the individual--something that has virtually no oppurtunity to change.

And why is I.Q. supposed to be stable? It seems you have a mistaken notion there as well. It measures performance on tasks that have high correlation with factors, as I have stated before. Why would you assume that I.Q. is supposed to be a stable measure?

The analogy illustrates the point that you don't discredit an instrument just because measurements vary. You need to investigate the reason for which the variations occur, rather than just jumping to the conclusion that it's an "invalid" instrument, which it wouldn't be in that case either - it'll simply be "unreliable".

I do believe you're very confused as to what direction the discussion started in and is headed in. In any case, as I've mentioned, I'm wasting my time if I continue this so this will be my last post in this thread, regarding this.

 

[Dickfore]

just him, not me

btw, we have 3, 8, 18, 30, 70

if we add each number to the next one, we end up with:

11, 26, 48, 100

repeating it with this result, we end up with:

37, 74, 148

so, we have each term multiplying by 2 to get the next, which means the next term in this is 296

working backwards, we end up with 126 for the next term in the original sequence

So you are effectively saying that:

<br /> b_{n} \equiv a_{n} + a_{n + 1}<br />

<br /> c_{n} \equiv b_{n} + b_{n +1}<br />

<br /> c_{n + 1} = 2 c_{n}<br />

Expressing c_{n} in terms of the original sequence a_{n}, we have:

<br /> c_{n} = (a_{n} + a_{n + 1}) + (a_{n + 1} + a_{n + 2}) = a_{n} + 2 a_{n + 1} + a_{n + 2}<br />

ans substituting this into your recursion relation:

<br /> a_{n + 1} + 2 a_{n + 2} + a_{n + 3} = 2 \left( a_{n} + 2 a_{n + 1} + a_{n + 2} \right)<br />

<br /> a_{n + 3} - 3 a_{n + 1} - 2 a_{n} = 0<br />

This is a third order homogeneous recursion and I found it on page 2:

I have found that the sequence of these 5 numbers satisfies the following recursion:

<br /> x_{n + 3} = 3 x_{n+1} + 2 x_{n} <br />

Indeed:

<br /> 3 \times 8 + 2 \times 3 = 24 + 6 = 30<br />

<br /> 3 \times 18 + 2 \times 8 = 54 + 16 = 70<br />

We can conclude that the next number is:
<br /> x = 3 \times 30 + 2 \times 18 = 90 + 36 = 126<br />

So, my guess is that the next nymber in the sequence is 126.

Unfortunately, this is not the quoted solution, namely 150.