Let the sequence defined by: a = 1, a2 = 8, an = an-1 + 2an-2...

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Let the sequence defined by: a₁ = 1, a2 = 8, an = an-1 + 2an-2 for n ≥ 3 Prove that: an = 3 x 2n-1 + 2(−1)n for all n € N a) What is the Inductive hypothesis? b) What do you need to prove in Induction Step? c) Construct the whole proof with the proof structure. Let the sequence defined by: a₁ = 1, a2 = 8, an = an-1 + 2an-2 for n ≥ 3 Prove that: an = 3 x 2n-1 + 2(−1)n for all n € N a) What is the Inductive hypothesis? b) What do you need to prove in Induction Step? c) Construct the whole proof with the proof structure.