What term is used to describe compliance with an initial small request followed by compliance with a larger request?

Answer: Foot-in-the-door (FITD) mechanism

Explanation:

Foot-in-the-door mechanism is defined as the technique that followed by people to make others agree on a major or larger request by initially starting to make others agree on smaller request. This type of persuasion technique creates link between persuader and respondent.

This is a compliance method for persuading and making them agree upon the desired request. Respondent's negative reply on large request in this case is usually related with the slamming of door on the face.