5
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5, 10, 6.5, 8.5, 8, 7, 9, 5.5, 5,

What is the next number in the sequence?

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    $\begingroup$ Hi radon and welcome to Puzzling :) I see you cross-posted this on Math.SE. There you say it was an interview question you didn't know the answer to - is this still the case: do you still not know the answer and are you hoping somebody here might be able to help you answer it? $\endgroup$ – Stiv Jul 2 '20 at 11:18
  • $\begingroup$ Hi @Stiv, thank you for the warm welcome :) I did not know the answer but now hexomino has answered it correctly. $\endgroup$ – Nitin Singla Jul 3 '20 at 6:22
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I'm wondering if there might be a typo in the sequence and it should read something like this

5, 10, 6.5, 8.5, 8, 7, 9.5, 5.5

This would involve swapping the last two commas for periods and the last period for a comma.
The reason I suggest this is that now the sequence follows a nice pattern

5 + 10 - 6.5 = 8.5
10 + 6.5 - 8.5 = 8
6.5 + 8.5 - 8 = 7
8.5 + 8 - 7 = 9.5
8 + 7 - 9.5 = 5.5
7 + 9.5 - 5.5 = 11

So the next term in the sequence would be 11

The other idea I had was that

We ignore elements of the sequence in the odd positions to get

_, 10, _, 8.5, _, 7, _, 5.5, _

Then we see that the elements in even positions follow an arithmetic sequence and the next element should be 4.

I don't prefer this one though because it involves dropping half of the elements.

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    $\begingroup$ I spotted that exact same half-pattern (your second idea). It would be disappointing if it turned out to be correct with half the information unused, but it could very easily be a case of a mis-remembering by the OP or just a poorly concocted interview question... $\endgroup$ – Stiv Jul 2 '20 at 16:45
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    $\begingroup$ @Stiv yes, the second one does not seem likely. I thought the typo theory might be legitimate as an interview candidate generally only has a small amount of time to answer a question and introducing a sequence with no reasonably deducible structure seems very unfair. $\endgroup$ – hexomino Jul 2 '20 at 16:48
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    $\begingroup$ I thought the same, hadn't noticed the additive relationship, but you can express the same sequence as two sequences where the first is incrementing by +1.5 and the second by -1.5. $\endgroup$ – MrSethward Jul 2 '20 at 16:51
  • $\begingroup$ @hexomino - Yes, typo theory is legitimate, my bad. Sincere thanks for answering. Your other idea also seems reasonable but is not the answer. I have accepted the answer for your first idea. $\endgroup$ – Nitin Singla Jul 3 '20 at 6:41
  • $\begingroup$ @MrSethward - Your answer is also accepted! $\endgroup$ – Nitin Singla Jul 3 '20 at 6:48

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