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(Solved): Suppose that \( a_{n} \) is defined by setting \( a_{1}=-2, a_{2}=0 \), and \( a_{n}=4 a_{n-1}-4 a ...



Suppose that \( a_{n} \) is defined by setting \( a_{1}=-2, a_{2}=0 \), and \( a_{n}=4 a_{n-1}-4 a_{n-2} \), where \( n \geq

Suppose that \( a_{n} \) is defined by setting \( a_{1}=-2, a_{2}=0 \), and \( a_{n}=4 a_{n-1}-4 a_{n-2} \), where \( n \geq 3 \). Using strong induction, prove that \( a_{n}=2^{n}(n-2) \) for all \( n \in \mathbb{Z}^{+} \).


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