Cite no less than three prominent examples of the repeating cycles that shape the plot of Invisible Man, and explain how Ralph Ellison uses this cyclical motif to articulate his broader critique.

One repeating cycle in Invisible Man is the narrator's habit of placing trust in powerful (usually white) authority figures, only to be let down or betrayed by them.
In the first chapter, the narrator recounts his high school graduation. After giving his valedictorian speech to his classmates, he is invited to present the same speech to a group of white leaders in the town. He believes that this is an opportunity to gain respect from these white leaders, and he thinks that they are giving him an opportunity to interact on a semi-equal level. These hopes are dashed when he appears and learns that the leaders are actually planning to make the narrator and a group of other black graduates engage in a "battle royale" for the amusement of the white leaders. The narrator is disillusioned both with the ploy and with his own internal desire to find the approval of these individuals by going along with their desires.
Once in college, the narrator gains the opportunity to act as a driver and guide for the white donors of the school. He views this as an opportunity to gain some respect and learn how to interact with white people. While driving a donor around the town, he accidentally takes the donor to the poor side of town and feels constrained to follow the donor's orders to keep moving forward. This leads to the donor interacting with an African American man that the school believes is a detrimental example to the race and to a visit to a local bar with a rough atmosphere. The narrator is sent away by the leader of the school, though he is given a set of letters that are to be given to specific donors in New York in order to help the narrator obtain a job. The narrator is grateful for this offer and heads out. Only after handing out all of the letters does the narrator learn that the college leader had lied to him and had actually made sure the narrator would not obtain a job. This leads the narrator to become disillusioned with the college leader and, by extension, the African American leaders of the time.
After some misadventures, the narrator defuses a near-riot with a powerful speech and is contacted by members of the Communist Party. They offer him the opportunity to give speeches in favor of Communism in order to better the condition of the poor. He believes that this will help remove some of the racism that exists in society while also helping to pull African-Americans out of poverty. However, he learns that the Communist Party is uninterested in dealing with racism and only wanted the narrator so they could have a black figurehead for political messaging. This leads the narrator to become disillusioned with self-professed white allies in the Communist and Socialist parties.
Ralph Ellison uses this motif to demonstrate that racism is pervasive in American society and that African-Americans will always fail to find themselves if they constantly look to the supporters of white America. The narrator has difficulty determining who he is and what he should do. During each cycle, he tries to find those answers through someone else. Each time he becomes disillusioned when he discovers that these answers are not helpful to him and that he has been used for selfish purposes. Ultimately, Ralph Ellison is trying to make the case that an individual must find his own answers if they are to have any real value.