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Duas for sitting in a gathering.
Fill the sitting with forgiveness, and close it with glorification

The Prophet ﷺ would ask forgiveness many times in a single sitting, and he closed his gatherings with words he described as an expiation for whatever was said in them.

2 sourced Du'as Arabic, transliteration, meaning, and source
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Closing a gathering: kaffarat al-majlis

سُبْحَانَكَ اللَّهُمَّ وَبِحَمْدِكَ، أَشْهَدُ أَنْ لاَ إِلَهَ إِلاَّ أَنْتَ، أَسْتَغْفِرُكَ وَأَتُوبُ إِلَيْكَ

Subhanaka-llahumma wa bihamdik, ash-hadu an la ilaha illa ant, astaghfiruka wa atubu ilayk.

“Glory be to You, O Allah, and all praise is Yours. I bear witness that there is no god but You. I ask Your forgiveness and turn to You in repentance.”

Jami at-Tirmidhi 3433 (sahih), Sunan Abi Dawud 4859 (hasan sahih)

Said before rising from a gathering. The Prophet ﷺ called it an expiation for whatever was said in it.

Du'a 2 · Hisn al-Muslim

In a gathering: Rabbi-ghfir li wa tub 'alayya

عَنِ ابْنِ عُمَرَ رضي الله عنه قَاَلَ: كَانَ يُعَدُّ لِرَسُولِ اللَّهِ صلى الله عليه وسلم فِي الْمَجْلِسِ الوَاحِدِ مِائَةُ مَرَّةٍ مِنْ قَبْلِ أَنْ يَقُومَ: رَبِّ اغْفِرْ لِي، وَتُبْ عَلَيَّ، إِنَّكَ أَنْتَ التَّوَّابُ الغَفُورُ

'An Ibn 'Umar radiya-llahu 'anhu qal: kana yu'addu li-Rasulillahi sallallahu 'alayhi wa sallam fil-majlisil-wahidi mi'atu marratin min qabli an yaqum: Rabbighfir li, wa tub 'alayya, innaka antat-Tawwabul-Ghafur.

“Ibn 'Umar said: In a single sitting, the Messenger of Allah ﷺ would be counted saying a hundred times before he stood up: My Lord, forgive me and accept my repentance. Truly You are the Accepter of repentance, the Forgiving.”

Jami at-Tirmidhi 3434 (sahih), Sunan Abi Dawud 1516 (sahih), Sunan Ibn Majah 3814 (sahih)

The du'a itself is Rabbighfir li wa tub 'alayya, innaka antat-Tawwabul-Ghafur. Abu Dawud and Ibn Majah end it with at-Tawwabur-Rahim.