Problem 4 Part 1 Consider the recurrence relation a n 4a n 1 4a n 2 a Find the general solution to the recurrence relation (beware the repeated root) b Find the solution when a 0 1 and a 1 2 c Find the solution when a 0 1 and a 1 8 Part 2 Suppose that r n and q n are both solutions to a recurrence relation of the form a n a n 1 a n 2 Prove that c r n d q n is also a solution to the recurrence relation, for any constants c, d

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Question: Problem 4 Part 1. Consider the recurrence relation a n = 4a n-1 4a n-2 . a. Find the general solution to the recurrence relation

Problem 4 Part 1. Consider the recurrence relation a_n = 4a_n-1 4a_n-2.

a. Find the general solution to the recurrence relation (beware the repeated root).

b. Find the solution when a₀ = 1 and a₁= 2.

c. Find the solution when a₀ = 1 and a₁ = 8.

Part 2. Suppose that r_n and q_n are both solutions to a recurrence relation of the form a_n = a_n-1 + a_n-2. Prove that c r_n + d q_nis also a solution to the recurrence relation, for any constants c, d.

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