Given a pattern:
0, 1, 2, 0.5, 2, 3, 5, 1, 2, 0, 2, 1, 4, 2, 3, $n$
Find the next item at $n$.
Pattern/sequence explanation required
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1 Answer
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4
Answer is
2.
Explanation:
For each $k$, the $4k$th term is the sum of the $(4k-3)$th and $(4k-2)$th terms divided by the $(4k-1)$th term. Thus: (0+1)/2=0.5; (2+3)/5=1; (2+0)/2=1; (4+2)/3=2.
I got this answer by noticing that 0,1,2 and 2,3,5 are the starts of well-known sequences, so it seems likely that the $4k$th term is always a fixed function of the preceding 3 terms.
answered May 2, 2015 at 20:34
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$\begingroup$ Correct! And under 2 minutes?.. Nice job. $\endgroup$ Commented May 2, 2015 at 20:38
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$\begingroup$ @zachgates7 Gotta get in there quick before someone else does! :-) I've done it before today as well. There should be a badge for this... $\endgroup$ Commented May 2, 2015 at 20:44
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$\begingroup$ There certainly should be! More sequences are on the way :-) $\endgroup$ Commented May 2, 2015 at 20:45
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$\begingroup$ @ZachGates I raised the possibility of having a badge for this, but apparently people don't like it... $\endgroup$ Commented May 5, 2015 at 7:53