A sequence \( x_{0}, x_{1}, x_{2}, x_{3}, \ldots \) is defined by letting \( x_{0}=5 \) and \( x...

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A sequence \( x_{0}, x_{1}, x_{2}, x_{3}, \ldots \) is defined by letting \( x_{0}=5 \) and \( x_{k}=4+x_{k-1} \) for all natural numbers \( k \). Show that \( x_{n}=5+4 n \) for all \( n \in N \) using mathematical induction.
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