A question regarding forgetfulness in prayer

Question:
I caught up with the imam for two rak'ahs of the four-rak'ah prayer, then the imam added a rak'ah out of forgetfulness, so I ended up praying three rak'ahs with the imam. Should I complete the two rak'ahs that I missed, or should I pray only one rak'ah? The imam said the closing salam without performing the prostration for forgetfulness, and when one of the worshippers reminded him, he turned back toward the qiblah and performed the prostration for forgetfulness. In that situation, I was still standing, completing the rak'ahs I had missed, and I did not perform the prostration for forgetfulness with the imam.

Answer:
You must make up the two rak'ahs that you did not catch up with the imam, and then perform the prostration for forgetfulness. As for the rak'ah that the imam added out of forgetfulness, it is not counted.