# Finish The Pattern #2

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

## 1 Answer

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.

• Correct! And under 2 minutes?.. Nice job. May 2 '15 at 20:38
• @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... May 2 '15 at 20:44
• There certainly should be! More sequences are on the way :-) May 2 '15 at 20:45
• @ZachGates I raised the possibility of having a badge for this, but apparently people don't like it... May 5 '15 at 7:53