2. Recursive Definitions (12 points) (1) (4 points) Write down the first 6 elements of the following sequence (where n E Z+), then give a recursive definition for an. Do not forget the base case. (You do not need to prove it is correct) (a) an = 4n-2 (b) an = 1+(-1)" C) an n (2) (4 points) See the bottom of page 180 of the textbook (Rosen, 7th edition) for a definition of A" for a square matrix A. Note that fk is the kth Fibonacci number. Define A as follows: Prove the following using weak induction: n+1 Jn n fn-I (3) (4 points) Give a recursive algorithm to compute the maximum ele- ment of an array of n integers. Also give the initial call to your recursive algorithm