Dear Professor Peabody,
I was unfortunately unable to take your midterm this past week due to a broken arm. I will not be able to write for the next 3 weeks. I am sending you this email asking you if there is any way that I would be able to make up your midterm. It would be greatly appreciated if I can make it up in any way. I am sorry to bother you, and I thank you very much for taking the time to read this email. I will awaiting your reply.
Thank You Very Much,