# How to find the formula for these repeating sequences?

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..

• 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 $3,6,5,2,3,3,6,5,2,3,3,6,5,2,3,\dots$? – bof Nov 30 '14 at 6:33
• it is 3, 6, 5, 2, 3, 6, 5, 2, 3, 6, 5 ,2 and so on – once Nov 30 '14 at 7:06
• $4-2\cos(\frac{n\pi}2)-\sin(\frac{n\pi}2)$ – bof Nov 30 '14 at 7:21
• wowwww...How did you find it? Could you clarify the formula for me? Thank you so much :-) – once Nov 30 '14 at 8:02
• 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 $B$. – bof Nov 30 '14 at 8:31