Please show all steps to solve the problems in detail.

5. The following pseudocode computes the sum of an array of n integers. int sum (int A , int n) T = A[0] for i= 1 to n-1 return T; (a) Write a recursive version of this code. (b) Let f(n) be the number of additions performed by this computation. Write a recurrence equation for f(n). (Note that the number of addition steps should be exactly the same for both the non- recursive and recursive versions. In fact, they both should make exactly the same sequence of addition steps.) (c) Prove by induction that the solution of the recurrence is f(n) n-1 6. The following pseudocode finds the maximum element in an array of size n int MAX (int Al, int n) { M = A101 for i = 1 to n-1 if i] > M) M = A[i] // Update the max return M; (a) Write a recursive version of this program