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1. (10 points) Consider the following recurrence relation: A(0) = 1, A(1) = 4, A(n) = 3A(n 1) + 4A(n 2) for n 1 Use

1. (10 points) Consider the following recurrence relation:

A(0) = 1, A(1) = 4, A(n) = 3A(n 1) + 4A(n 2) for n 1

Use the guess and check method to guess a closed form for A(n) and then prove that it is a closed form for A(n) using mathematical induction.

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