there're some problems about sequence of number that are solve by using the characterristic equation, but i don't full understand the principle. for e.g : It is said that:

. a sequence of number X(n+2)=C1X(n+1)+C2X(n)

given r，s then X(n+2)-rX(n+1)=s[X(n+1)-rXn]

so X(n+2)=(s+r)X(n+1)-srXn

C1=s+r

C2=-sr

then eliminate s , then we got the so-called characterristic equation will be : r*r-C1*r-C2=0

I just don't understand that how can the 'S' can be eliminated, since X(n+2), Xn and X(n+1) can' t be combined?

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