Substituting x^2 for an+2, x ^1 for an+1 and x^0 for an,we get the equation,
x^2 -3x + 2 =0
roots of the above equation are 1,2
Therefore,characteristic equation will be,
an=c1(1)^n + c2(2)^n where c1,c2 are constants;
Substituting the value of n=0 and n=1,we get c1=-1 and c2=1;
Therefore, an=2^n-1
Hence (b)