We will find the solution to the following lhcc recurrence:
an=−2an−1+3an−2 for n≥2 with initial conditions a0=4,a1=7
The first step in any problem like this 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:
r^(n)=−2r^(n−1)+3r^(n−2.)
Since we are assuming r≠0 we can divide by the smallest power of r, i.e., r^(n−2) to get the characteristic equation:
r^(2)=−2r+3
(Notice since our lhcc recurrence was degree 2, the characteristic equation is degree 2.)
Find the two roots of the characteristic equation r1 and r2. When entering your answers use r1≤ r2:
r1=
r2=