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[See Steps] A sequence is defined recursively as follows: ∀ k≥ 1,a_k=4*a_k-1+1 , a_0=2 , Find an explicit formula for this sequence. Prove your

Question: A sequence is defined recursively as follows:

\[\begin{aligned} & \forall k\ge 1,{{a}_{k}}=4*{{a}_{k-1}}+1 \\ & {{a}_{0}}=2 \\ \end{aligned}\]
  1. Find an explicit formula for this sequence.
  2. Prove your formula by induction.

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