2. Pseudocode and Loop Invariant: (20 points) textbook, Exercise2.1-3, p22, Linear Search. 2.1-3 Consider the searching problem: (a1, a2, ..., an) and a value v. Input: A sequence of n numbers A = Output: An index i such that v = A[i] or the special value NIL if v does not appear in A. Write pseudocode for linear search, which scans through the sequence, looking for v. Using a loop invariant, prove that your algorithm is correct. Make sure that your loop invariant fulfills the three necessary properties