Final answer:
The correct word to complete the sentence is 'punished,' as grounding someone is a form of punishment for an action, in this case, skipping a class.
Step-by-step explanation:
The correct answer to the question 'Brother Jacques ______ Archie for skipping Latin by grounding him for the semester' is option a. Punished. In this context, grounding someone for a semester is a form of punishment, therefore, the correct word to fill in the blank is 'punished'. The act of grounding is used as a disciplinary measure which means to enforce rules or restrictions upon someone as a result of their actions. Therefore, rewarding, encouraging, or excusing do not fit the context of grounding as a consequence for skipping a class.