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Fill in the correct number in this sequence:

5 3 8 9 1 27 ?

The options are: 18, 54, 38, 14 or 13.

I can see the pattern of 3, 9, 27 but other than that I am clueless.

Source: a publicly available practice test in a book for an IQ-test I got via a friend in the Netherlands.

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    $\begingroup$ I added more explanation on the source. $\endgroup$
    – Dennispuz
    Commented Nov 16, 2018 at 12:34
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    $\begingroup$ Upon first observation, it seems like there are two sequences; there is the 3, 9, 27 pattern alternating with a pattern that adds three to each term, ignoring the tens. Unfortunately, the answer must apparently include tens so that is a circumstantial relationship. $\endgroup$
    – kanoo
    Commented Nov 16, 2018 at 21:12
  • $\begingroup$ I also noticed that the sequence includes each digit between 1 and 9 exactly once, except 4 and 6, in case that means anything. $\endgroup$
    – kanoo
    Commented Nov 16, 2018 at 21:13
  • $\begingroup$ It seems I found similar question without 27.. According to the Online Encyclopedia of Integer Sequences: oeis.org/search?go=Search&language=english&q=5,3,8,9,1.. next number is sequence might be 1 or 3.. $\endgroup$
    – CR241
    Commented Nov 22, 2018 at 0:13
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    $\begingroup$ @Dennispuz You completely missed my point. If 1 really was part of the sequence, those other options would make no sense at all. But with 11, they at least make some sense (as wrong answers). It's only because you now know that 14 is the correct answer that you can say that the other options are wrong, and why. Before that, you were "clueless" (according to your question). Those other options will only mislead someone who doesn't already know the answer. $\endgroup$
    – ekhumoro
    Commented Jan 3, 2019 at 0:11

3 Answers 3

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i think the answer is 14 because, in odd position 581=40, in even position 3927=729. then you add 40 to 729= 769. then 769 -53 ( obtained by adding the numbers of the sequence) = 716. 7+1+6 you obtain 14. or you can 3927= 729 then 7+2+9=18, 581=40 you obtain 4. 18-4=14

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    $\begingroup$ Can you explain why you would do all of these things? Can we produce previous numbers in the sequence in a similar way? $\endgroup$
    – hexomino
    Commented Sep 30, 2020 at 10:02
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One way of thinking about it would be

to observe that none of the sequence have distinct prime factors. Of the choices given the only one preserving this property is $13$.

This would mean that the problem is only solvable because of the specific set of choices provided.

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By visual inspection we see $3^1,3^2,3^3$ form an ascending sequence of powers of 3. The five given numbers cannot be the next term of this sequence. The numbers $5,1$ are divisible by themselves but $8$ is a composite number. I say the answer is $14$ because $5+1+8=14$.

If the missing number is $14$, then the numbers $18,54,38,14$ have a common factor, the number $2$. In addition to that, by subtraction of these numbers we obtain the squares $54-38=2^4$ and $18-14=2^2$.

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