I apologize for cutting class on {day}. I have no excuse. It was an impulsive decision, and one that I regret.
I respect you as a teacher and while it may not seem like it based on this behavior, I really am learning a lot in your class. I've been studying hard for the {topic} test and I hope I can redeem myself to some small degree.
Although I did receive {detention/punishment}, this letter has nothing to do with that. I genuinely regret not showing up to class, and I realize now how disrespectful it was to cut. I take my education very seriously and appreciate your instruction.
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Index of letter of apology templates