All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is not an obligation to recite these chapters and verses with the order that is mentioned in the question; rather, it is more appropriate to follow the order of the Mus-haf (the Arabic text of the Quran). However, following the order of the Mus-haf is not an obligation according to the view of the jurists whether during the prayer, when performing Ruqyah, in lectures or else. Huthayfah said: “I prayed with the Prophet one night and he started reciting Chapter Al-Baqarah [Quran 2]. I thought that he would make Rukoo’ (bow down) at the end of one hundred verses, but he continued reading; I then thought that he would perhaps recite the whole Chapter before making Rukoo' (i.e. in the second Rak'ah), but he continued reading and I thought he would perhaps make Rukoo’ on completing this Chapter. He then started Chapter An-Nisa' [Quran 4], and recited it; he then started Aal 'Imran [Quran 3] and recited leisurely….”
An-Nawawi said when commenting on this Hadeeth which was reported in Saheeh Muslim: “Al-Qaadi Iyaad said: “This contains evidence supporting the view of those who say that the order of the chapters of the Quran (Surahs) is the result of Ijtihaad on the part of the Muslims when they wrote down the Mus-haf and that it was not the sequence set by the Prophet ; rather, he [the Prophet ] entrusted this matter to his nation after him. He [Al-Qaadi Iyaad] said: “This is the view of Maalik and the view of the majority of the scholars, and this is also the view chosen by Al-Qaadi Abu Bakr Al-Baaqillaani . Ibn Al-Baaqillaani said: “It is the most correct of the two opinions, although both of them are probable. He said: “What we say here is that the order of the Surahs is not binding when writing, praying, studying, teaching or learning, as there is no text (regarding this) or a limit from the Prophet which we are forbidden to violate.”
Allaah Knows best.