Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 7 Marks

Year: Dec 2015

The characteristic equation of the recurrence relation is $r^2-5r+6=0$

Its roots are $r_1=3, r_2=2$. Hence the sequence {$a_n$} is a solution to the recurrence relation if and only if

$a_n=α_1*3^n+α_2*2^n$

For some constant $α_1$ and $α_2$.

From the initial condition, it follows that

$a_0=-1=α_1 + α_2 \\ a_1= 1 = 3α_1 + 2α_2$

Solving the equations, we get $α_1=3, α_2=-4$

Hence the solution is the sequence {$a_n$} with $$a_n =3*3^n-4*2^n$$