A sequence (bn)n∈N is defined recursively by b1 = 1, b2 = 2, and bn = bn−1 + 2bn−2, and for n ≥ 3. Conjecture an explicit formula for bn in terms of n alone (not recursively). For example your : conjecture should be an explicit formula such as bn = 2n + 1 or bn = n . Note both of these conjectures are wrong. and By induction, prove your formula for bn in the previous part is true for all n ∈ N.