# What is the next number in this sequence? [closed]

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!!

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

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Antonios-Alexandros Robotis, José Carlos Santos, user91500, Martin R, Claude Leibovici
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• When asked in math SE, any number may comply. Asked on puzzling you can get some answers as below. – z100 Aug 10 '17 at 9:53

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 $10$.

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

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

$a_9 = ?$

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

$a_{10} = ?$

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

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

$a_9= ?$.