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How to find formula for this number pattern?

3,6,5,2,3,...

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

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  • $\begingroup$ 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
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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.

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