The sequence $(y\_n)$ satisfies the relationship ${y\_{n-1}}{y\_{n+1}} + y\_n = 1$ for all $n \ge 2$. If $y\_1= 1$ and $y\_2= 2$, What can you say about the sequence? What happens for other starting values?



Sequence problem find its character
For arbitrary Initial values $y\_1=a,y\_2=b$ (with $ab$ not zero) you get $a,b, \frac{1-b}{a},\frac{a+b-1}{ab},\frac{1-a}{b}$ . Then the sequence is periodic with period 5.
Thus for $y\_1=1,y\_2=2$ the sequence should be $1,2,-1,1,0,1,2,-1,1,0,\dots.$


