Both "The motivation" and "A motivation" can be correct, depending on the context. Use The motivation when you are referring to a specific* motivation that has already been mentioned or is understood by both the speaker and listener. Example: "We discussed several reasons for his decision. The motivation* behind his actions was clear." (Referring to a specific, previously discussed motivation.) Use A motivation when you are referring to one* motivation among possibly many, or when introducing a motivation for the first time. Example: "He had a motivation* to succeed." (Referring to one of potentially many motivations, or introducing it generally.) So, the choice depends on whether you're talking about a specific, known motivation or any motivation.