Transcription of HOMEWORK 8 SOLUTIONS PART A - Cornell University
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HOMEWORK 8 SOLUTIONS PART A - Cornell University
HOMEWORK 8 SOLUTIONS part A 1.(a) an = an-1+ 6 an-2 , a0 = 3, a1 = 6 The characteristic equation of the recurrence relation is r2 -r -6 = 0 Its roots are r= 3 and r= -2. Hence the sequence {an} is a solution to the recurrence relation if and only if an = 1 3n+ 2 (-2)n for some constant 1 and 2. From the initial condition, it follows that a0 = 3 = 1 + 2 a1 = 6 = 3 1 - 2 2 Solving the equations, we get 1= , 2 = Hence the solution is the sequence {an} with an = (3n)+ (-2)n (b) an = 7 an-1 -10 an-2 , a0 = 2, a1 = 1 The characteristic equation of the recurrence relation is r2 -7r +10 = 0 Its roots are r= 2 and r= 5. Hence the sequence {an} is a solution to the recurrence relation if and only if an = 1 2n+ 2 5n for some constant 1 and 2.
HOMEWORK 8 SOLUTIONS PART A 1.(a) a n = a n-1+ 6 a n-2 , a 0 = 3, a 1 = 6 The characteristic equation of the recurrence relation is r2 -r -6 = 0 Its roots are r= 3 and r= -2. Hence the sequence {a n} is a solution to the recurrence relation if and only if a n =
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