Protreptical is an adjective used to describe something that serves as an invitation or persuasion to take action. There are several synonyms for this word that can be used in different contexts. One synonym is persuasive, which refers to something that has the ability to convince or influence others. Another synonym is encouraging, which suggests providing support or motivation to someone. Similarly, appealing is another synonym that means attractive or interesting enough to make someone want to take action. Alternatively, stimulating can also be used to describe something that arouses or excites interest or encourages action. Finally, inspiring is another synonym that suggests the ability to create a positive impact and motivate someone towards a particular goal or action.