Final answer:
The worst-case time complexity for finding the index of the first item with a particular value in an array-based list implementation is O(n), assuming a linear search algorithm is used.
Step-by-step explanation:
When discussing an array-based implementation of a list and the task of finding the index of the first item with a particular value, we refer to a linear search algorithm. In the worst-case scenario, you must traverse the entire array to find the item or conclude that the item doesn't exist in the array. Thus, the time complexity for this operation is O(n), where n is the number of items in the list. This is because in the worst case, each item must be checked once until the particular item is found or the end of the list is reached without finding the item.