Final answer:
The author's purpose in a text that encourages the reader to believe or do something is to persuade.
Step-by-step explanation:
The author's purpose in a text that encourages the reader to believe or do something is to persuade. When an author wants to persuade the audience, they are aiming to convince the readers of a particular idea or action. This could be seen in persuasive writing, where the purpose is usually revealed in a thesis statement that defines the author's position and provides reasons for it.