[Step-by-Step] A sequence b_1, b_2, b_3, ... satisfies the recurrence relation b_k=2 b_k-1+8 b_k-2 with initial conditions b_1=1 and b_2=0. Find an explicit formula
Question: A sequence \(b_{1}, b_{2}, b_{3}, \ldots\) satisfies the recurrence relation \(b_{k}=2 b_{k-1}+8 b_{k-2}\) with initial conditions \(b_{1}=1\) and \(b_{2}=0\). Find an explicit formula for the sequence. Show your work to find the formula.
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