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What is the next number in this sequence? 2, 1, 4, 2, 6, 4, 8, 8

Possible answers: 6, 8, 10, 12, 16

I wrote it all down and at 8,8 the pattern confuses me. I really appreciate your help, i've struggeling for a few days with this sequence.

Thnx!!

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closed as off-topic by Antonios-Alexandros Robotis, José Carlos Santos, user91500, Martin R, Claude Leibovici Aug 10 '17 at 10:28

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  • 2
    $\begingroup$ When asked in math SE, any number may comply. Asked on puzzling you can get some answers as below. $\endgroup$ – z100 Aug 10 '17 at 9:53
2
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Hint: take alternate terms from the sequence.

Further hint:

The sequence can be split into two interleaved subsequences: $2,4,6,8,\ldots$ and $1,2,4,8,\ldots$. The next term must come from the first subsequence, so it is $10$.

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0
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It's 10. The sequence is $$x_{2n+2}=x_{2n}+2\quad \text{and}\quad x_{2n+1}=2x_{2n-1}.$$

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$a_1 = 2; a_3 = 4; a_5 = 6, a_7= 8,$

$a_9 = ?$

$a_2 = 1; a_4 = 2; a_6= 4; a_8= 8,$

$a_{10} = ?$

$a_{2k+1} = 2k+2, k=0,1,2,...$

$a_{2k+2} = 2^k, k=0,1,2,...$

$a_9= ?$.

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