A man after his death, experiences elevation with Allah. He asks Allah (swt) where is this coming from? Allah (swt) says you are experiencing this because your son made dua for you. 

When you are thinking about duas to say the main one is asking forgiveness.  We hear that a person was good, but we do not know everything about them.  We keep hope that the person will enter jannah. Every time we ask forgiveness it either wipes out our sins or elevates our rank. 

What are the best duas to recite for those who have passed away? What are the sequences we can derive even for our own personal duas?

The best du’as for the deceased: ‏ اللَّهُمَّ اغْفِرْ لَهُ وَارْحَمْهُ وَعَافِهِ وَاعْفُ عَنْهُ وَأَكْرِمْ نُزُلَهُ وَوَسِّعْ مُدْخَلَهُ وَاغْسِلْهُ بِالْمَاءِ وَالثَّلْجِ وَالْبَرَدِ وَنَقِّهِ مِنَ الْخَطَايَا كَمَا يُنَقَّى الثَّوْبُ الأَبْيَضُ مِنَ الدَّنَسِ

Oh Allah, forgive him and have mercy on him and give him strength and pardon him. Be generous to him and cause his entrance to be wide and wash him with water and snow and hail. Cleanse him of his transgressions as white cloth is cleansed of stains. 

 اللَّهمَّ اغْفِرْ لِحَيِّنَا وَمَيِّتِنَا وَشَاهِدِنَا، وَغَائِبِنَا، وَصَغِيْرِنَا وَكَبِيْرِنَا، وَذَكَرِنَا وَأُنْثَانَا. اللَّهمَّ مَنْ أَحْيَيْتَه ُُ مِنَّا فَأَحْيِه ِِ عَلَى الإِسْلامِ، وَمَنْ تَوَفَّيْتَه ُُ مِنَّا فَتَوَفَّه ُُ عَلَى الإِيْمَانِ، اللَّهمَّ لا تَحْرِمْنَا أَجْرَهُ، وَلا تُضِلَّنَا بَعْدَهُ 

 Oh Allah, forgive our living and our dead, those present and those absent, our young and our old, our males and our females. O Allah, whom among us You keep alive, then let such a life be upon Islam, and whom among us You take unto Yourself, then let such a death be upon faith. O Allah, do not deprive us of his reward and do not let us stray after him.

 اللَّهمَّ عَبْدُكَ وَابْنُ أَمَتِكَ، اِحْتَاجَ إِلَى رَحْمَتِكَ، وَأَنْتَ غَنِيٌّ عَنْ عَذَابِهِ، إِنْ كَانَ مُحْسِنا ً فَزِدْ فِي حَسَنَاتِه، وَإِنْ كَانَ مُسِيْئا ً فَتَجَاوَزْ عَنْهُ 

 Oh Allah, this son of a servant of yours is now in need of Your mercy and You are not in need of punishing that person. If he was pious then increase his rewards, and if he was a transgressor then pardon him.
  اللَّهُمَّ اغْفِرْ لأَبِي سَلَمَةَ وَارْفَعْ دَرَجَتَهُ فِي الْمَهْدِيِّينَ  وَافْسَحْ لَهُ فِي قَبْرِهِ ‏.‏ وَنَوِّرْ لَهُ فِيهِ وَاخْلُفْهُ فِي عَقِبِهِ فِي الْغَابِرِينَ وَاغْفِرْ لَنَا وَلَهُ يَا رَبَّ الْعَالَمِين 

 Oh Allah forgive Abu Salamah and raise his rank among those who are rightly-guided. Make his grave spacious for him and give him light in it and grant him a successor from his descendants who remain behind.