The sequence (gn) is defined recursively as follows: g₀=1, and g=3. g₁+2n, for n>1. If the theorem below is proven by induction, what must e established in the inductive step? Theorem: For any non-negative integer n, gn (5/2) 2"- n (3/2).
a. For ka0, if g 3 g2k, then g(5/2) 2k+¹- (k+) - (3/2).
b. For k20, if g (5/2) 2* - k- (3/2), then gk1(5/2) 2k1 - (k+1) (3/2).
c. For k20, if gk 3 gk-1 + 2k, then g3 gk + 2(k+1
d. For k2O, ifg-(52) 2'-k-(32), then gk+1-3 + 2(k+1).