How to find formula for this number pattern?


When plot this sequence into the graph, it is going to be the sine graph..

  • $\begingroup$ How does the rest of the sequence go? Is it $3,6,5,2,3,4,3,6,5, 4,4,\dots$? or is it $3,6,5,2,3,3,6,5,2,3,3,6,5,2,3,\dots$? $\endgroup$ – bof Nov 30 '14 at 6:33
  • $\begingroup$ it is 3, 6, 5, 2, 3, 6, 5, 2, 3, 6, 5 ,2 and so on $\endgroup$ – once Nov 30 '14 at 7:06
  • $\begingroup$ $4-2\cos(\frac{n\pi}2)-\sin(\frac{n\pi}2)$ $\endgroup$ – bof Nov 30 '14 at 7:21
  • $\begingroup$ wowwww...How did you find it? Could you clarify the formula for me? Thank you so much :-) $\endgroup$ – once Nov 30 '14 at 8:02
  • $\begingroup$ The terms average out to $4$, so I "guessed" the formula would be $4+A\cos(\frac{n\pi}2)+B\sin(\frac{n\pi}2)$, and then it was easy to solve for $A$ and $B$. $\endgroup$ – bof Nov 30 '14 at 8:31

There is no pattern. You can get any number you like to be the next in each sequence using infinitely many different formulae. See http://en.wikipedia.org/wiki/Polynomial_interpolation for one type of formulae that can be made to fit any sequence.


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.