Question 1208339
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Questions of this form and of this type are mathematically   {{{highlight(highlight(NONSENSICAL))}}}.



An arbitrary finite sequence of numbers does not indicate the next term 
and does not determine what the next term should be,
until a special separate procedure,  a formula or a rule specifies on how to determine the next term.


Therefore,  if and when any witch doctor/(woodoo doctor)/(charlatan) gives you a definite answer - know 
that you are either being screwed,  or deceived,  or mocked.


It is known and it is clear to anybody and to everyone, who has 
a bit of common sense in his or her brain inside his or her head.



The only correct answer to this question/problem and to million other  " problems "  of this kind is 


                "any number can be next term",


but it is,  obviously,  not what the asking person does expect.



So, please do not post nonsensical problems of this type to this forum in the future.



Thank you very much and have a nice day !



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Edwin, one standard approach to such problems is to make a row of first differences;

then below it to make next row of second differences

and so on until you get the row consisting of one unique number.


Then it is assumed (without having ani solid base) that all differences of certain order are constant,
and based on it, making backward steps, people restore the original function.


Or, in more simple terms, people simply request and find a polynomial approximation 
("exact fit") to the given sequence from online Internet solvers.


Then, using this polynomial, they calculate "the next number" and declare/demonstrate 
it as the ANSWER (without having any solid base for it).


The refutation to it is the fact, that we can add another polynomial to the first polynomial
which has zeroes at the given points 1, 2, 3, 4, but has an arbitrary value in the "next point #5".



This is the whole story and the whole tale.


Edwin, you invite me to bring this knowledge to other people.


The world is full of mathematically illiterate people. The number of them is billions.


To me, the TRUTH is clear from the first glance; but I will not spend my time and my efforts 

to bring/explain this truth to millions others, where and why they are wrong.  For it, they should 

have some adequate mathematical education, which they, as a rule, do not have.


How I can convince them, if during the years I can not convince you, who has a university Math education ?


For these people, my advise is to use good sources and do not use bad sources for their Math problems.



        Good sources are those that are written by specialists and professionals.

                Bad sources are those that are created by all others.



At this forum, the visitors regularly bring their problems "from garbage bins",

but I can do nothing against it  (unfortunately).



For such visitors, I only have this standard message, which is the first part
of my post.  I keep this message in my archive and use it to respond every time,
as the current nonsensical post/request comes.



Regarding this practice on giving such nonsensical problems as the test for getting jobs,

these people from HR departments deserve to be fired immediately, since they 

do not understand what they are doing and are not adequate to their positions.



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In the shortest words, this problem is a puzzle of the most low level - 
- of that kind what some charlatans give to unexperienced naive amateurs
to help them to kill their time and to get their money, giving them NOTHING back.


In such puzzles, a correct mathematical solution is impossible, is not required and even is not assumed.


What is required - are these two things:


        - (1)   amateurs kill their time in exact accordance with their most wanted hidden desire,  and they are very happy of it;


        - (2)   those who create these puzzles for them, leave the scene taking their money in their pockets,  and they are happy, too.


Everything else does not matter and does not play any role.


Everybody is satisfied and everybody is happy.



            Only me work here in the sweat of the face, 

            explaining you all details of this backstage.


<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;All such puzzles are {{{highlight(highlight(CHARLATANISM))}}} 
&nbsp;&nbsp;&nbsp;&nbsp;from the very beginning to the very end.</H3>



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Edwin, reading your post, I see that you are wonder, why two different logical 
reasoning to this puzzle lead to different results.


You should not be surprised. It is completely natural.


It is the same as if two different formulas, applied to 4 given numbers, would lead to different results.


Nobody has ever proved a theorem on the uniqueness of the solution of crazy puzzles.


It is absolutely natural that two different approaches, applied to the given set of input numbers lead to different results.



Simply, let me repeat it again, all this activity around this crazy puzzle is a kind of gibberish.



It is as clear to anybody in healthy mind as 2 x 2 = 4.