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

[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:

$$b_{n} \equiv a_{n} + a_{n + 1}$$

$$c_{n} \equiv b_{n} + b_{n +1}$$

$$c_{n + 1} = 2 c_{n}$$

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

$$c_{n} = (a_{n} + a_{n + 1}) + (a_{n + 1} + a_{n + 2}) = a_{n} + 2 a_{n + 1} + a_{n + 2}$$

ans substituting this into your recursion relation:

$$a_{n + 1} + 2 a_{n + 2} + a_{n + 3} = 2 \left( a_{n} + 2 a_{n + 1} + a_{n + 2} \right)$$

$$a_{n + 3} - 3 a_{n + 1} - 2 a_{n} = 0$$

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:

$$x_{n + 3} = 3 x_{n+1} + 2 x_{n}$$

Indeed:

$$3 \times 8 + 2 \times 3 = 24 + 6 = 30$$

$$3 \times 18 + 2 \times 8 = 54 + 16 = 70$$

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

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

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