"The recurrence relation for the worst-case time complexity of the merge sort algorithm is T(n) = T(n - 1) + n. To derive the time complexity, we solve for T(n) in terms of T(n - 1) and n, and then repeat the process to express T(n) in terms of a fixed number of iterations. We show that since each iteration takes time proportional to the size of the input array, the time complexity of the algorithm is O(n). Therefore, the worst-case time complexity of the merge sort algorithm is O(n^k), where k is the number of iterations required to sort the array."