= 3 · gn-1 + 2n, for n > 1. If the theorem %3D The sequence {9n }is defined recursively as follows: go = 1, and gn below is proven by induction, what must be established in the inductive step? 3 Theorem: For any non-negative integer n, gn = 2"-n - . O For k20, if gr = 3. gk-1 + 2k, then g+1 . 2차1-(k+ 1)-글 O For ke0, if gk 3D을. 2*-k-을, then g(+1) =D을 .2k+1-(k + 1)-을. 5. 2* - k -. then g(k+1) - 2*+1 – (k+1)- |3| O For k20, if gk = 3. gk-1 + 2k, then g+1 3. gk +2 (k+1). O For k20, if g=; 2* – k – , then g+1 = 3 · gk + 2 (k + 1). %3D

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