Wednesday, 10 April 2019
10:26 AM
Solve the recurrence −6a_(n−2)=12_files/image001.png){kind=small}
−6a_(n−2)=12_files/image002.png){kind=small}
−6a_(n−2)=12_files/image003.png){kind=small}
Find the homogeneous equation
−6a_(n−2)=12_files/image004.png){kind=small}
−6a_(n−2)=12_files/image005.png){kind=small}
−6a_(n−2)=12_files/image006.png){kind=small}
Roots are −6a_(n−2)=12_files/image007.png){kind=small}
So −6a_(n−2)=12_files/image008.png){kind=small}
Don't resolve A and B with the initial
conditions, as the initial conditions are for −6a_(n−2)=12_files/image009.png){kind=small}
Find the particular solution
RHS (12) is a constant, so try C
−6a_(n−2)=12_files/image010.png){kind=small}
Substitute
−6a_(n−2)=12_files/image011.png){kind=small}
−6a_(n−2)=12_files/image012.png){kind=small}
−6a_(n−2)=12_files/image013.png){kind=small}
Obtain the general solutions
−6a_(n−2)=12_files/image014.png){kind=small}
Resolve for A and B