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Solve the following recurrence relation:an5an1+6an2=0an5an1+6an2=2πwith initial conditionsa0=1  and  a1=1

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 7 Marks

Year: Dec 2015

1 Answer
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The characteristic equation of the recurrence relation is r25r+6=0

Its roots are r1=3,r2=2. Hence the sequence {an} is a solution to the recurrence relation if and only if

an=α13n+α22n

For some constant α1 and α2.

From the initial condition, it follows that

a0=1=α1+α2a1=1=3α1+2α2

Solving the equations, we get α1=3,α2=4

Hence the solution is the sequence {an} with an=33n42n

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