We will find the solution to the following lhcc recurrence: an=8an−1−16an−2 for n≥2 with initial conditions a0=4,a1=7. The first
step as usual is to find the characteristic equation by trying a solution of the "geometric" format an=rnan=rn. (We assume also r≠0). In this case we get: rn=8r^n−1−16r^n−2. Since we are assuming r≠0r≠0 we can divide by the smallest power of r, i.e., rn−2 to get the characteristic equation: r^2=8r−16. (Notice since our lhcc recurrence was degree 2, the characteristic equation is degree 2.)
This characteristic equation has a single root rr. (We say the root has multiplicity 2). Find r.
r=?
