1
$\begingroup$

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

$\endgroup$
3
$\begingroup$

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.

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.