Is it essential to recite the Quran in sequence for one who wants to complete it?

It is mustahabb to read Quran a great deal during Ramadaan, because it is the month of the Quran. Allah, may He be exalted, says (interpretation of the meaning): 

“The month of Ramadan in which was revealed the Quran, a guidance for mankind and clear proofs for the guidance and the criterion (between right and wrong)” [al-Baqarah 2:185].

Jibreel used to come to the Prophet (peace and blessings of Allah be upon him) every night in Ramadaan and review the Quran with him. Narrated by al-Bukhaari (5) and Muslim (4268). 

Al-Bukhaari (4614) narrated from Abu Hurayrah (may Allah be pleased with him) that Jibreel used to review the Quran with the Prophet (peace and blessings of Allah be upon him) once every year, and he reviewed it with him twice in the year when he died. This indicates that it is mustahabb to complete the Quran and study it in Ramadaan.

 Hence the salaf used to read Quran a great deal during Ramadaan, following the example of the Prophet (peace and blessings of Allah be upon him). Qataadah (may Allah have mercy on him) used to complete the Quran every seven nights all the time, and every three nights in Ramadaan, and every two nights during the last ten days of Ramadaan.  

Ibraaheem al-Nakha’i used to complete the Quran in Ramadaan every three nights, and in the last ten days every two nights. 

Al-Aswad (may Allah have mercy on him) used to read the entire Quran every two nights throughout the month. End quote from Majaalis Shahr Ramadaan by Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) p. 65. 

Secondly: 

The best is to read the Quran in the order of soorahs as given in the Mus-haf, which is the sequence in which Jibreel reviewed the Quran with the Prophet (peace and blessings of Allah be upon him) at the end of his life.  

See: al-Tahbeer fi ‘Ilm al-Tafseer by al-Suyooti, p. 637 

Al-Nawawi (may Allah have mercy on him) said in al-Tibyaan: 

The scholars (may Allah have mercy on them) said: The best is to read it in the order in which it appears in the Mus-haf, so he should read al-Faatihah, then al-Baqarah, then Aal ‘Imraan, then al-Nisa’, until he ends with Qul a’oodhu bi Rabbi l-naas (Sooratal-Naas), whether he is reciting it in prayer or otherwise. It is also mustahabb, if he recites one soorah, to recite after it the soorah that comes after it. So if he recites Qul a’oodhu bi Rabbi l-naas (Sooratal-Naas) in the first rak’ah, he should recite from al-Baqarah in the second. 

The evidence for that is that the order of soorahs given in the Mus-haf is for a reason, so that order should be followed, except in cases where it is narrated that there is an exception, such as in Fajr prayer on Friday, when Alif-Laam-Meem Tanzeel (Soorat al-Sajdah) is recited in the first rak’ah and Hal ata (Soorat al-Insaan) in the second, and the Eid prayers when Soorat Qaaf and Soorat al-Qamar may be recited. 

If he recites them in a different order and recites one soorah then recites a soorah that comes before it, or he recites a soorah that does not come straight after it, that is permissible, even if he is not doing what is best. As for reciting a soorah from the end to the beginning, there is no dispute that this is not allowed and is blameworthy, because it is a distortion that detracts from the linguistic miracle of the Quran and goes against the wisdom behind the order in which the verses appear. 

End quote from al-Nawawi. 

There is a report from ‘Aa’ishah which indicates that it is not obligatory to read Quran in sequence. 

Al-Bukhaari (4993) narrated that Yoosuf ibn Maahak said: I was with ‘Aa’ishah the Mother of the Believers when an Iraqi came to her and said: “O Mother of the Believers, show me your Mus-haf.” She said: “Why?” He said: “So that I may compile and arrange the Quran according to it, for people recite it with its soorahs not in proper order.” She said: “It does not matter which part you read first. The first part of it to be revealed was a soorah from al-Mufassal which mentioned Paradise and Hell, then when the people became steadfast in Islam, (rulings on) halaal and haraam were revealed. If the first thing to have been revealed was ‘Do not drink wine,’ they would have said: ‘We will never give up wine.’ If it had been revealed, ‘Do not commit zina,’ they would have said, ‘We will never give up zina.’ It was revealed in Makkah to Muhammad (peace and blessings of Allah be upon him) when I was a young girl playing, ‘Nay, but the Hour is their appointed time (for their full recompense), and the Hour will be more grievous and more bitter’ [al-Qamar 54:46]. And Soorat al-Baqarah and al-Nisa’ were not revealed except I was with him.” 

Al-Haafiz said: 

It seems to me that this Iraqi was one of those who followed the recitation of Ibn Mas’ood. When the Mus-haf of ‘Uthmaan was brought to Kufa, Ibn Mas’ood did not agree to recant his recitation or destroy his Mus-haf, and his compilation was different from that of ‘Uthmaan’s Mus-haf. (Compilation means the collection of the Mus-haf in order). Undoubtedly the compilation of ‘Uthmaan’s Mus-haf was more appropriate than any other, hence this Iraqi said that its soorahs were not in proper order. 

Ibn Battaal said: We do not know of anyone who regarded it as obligatory to recite the soorahs in order, whether during prayer or otherwise, rather it is permissible to recite al-Kahf before al-Baqarah, or al-Hajj before al-Kahf, for example. As for what is narrated from the salaf about it being forbidden to recite the Quran out of order, what is meant by that is reciting a soorah from its end to its beginning. There was a group which did that in poetry, to demonstrate their precise memorization thereof. So the salaf ruled that this is not allowed with regard to the Quran and it is haraam. Al-Qaadi ‘Iyaad said: The order of soorahs is not obligatory when reading or praying, or studying or teaching, hence Mus-hafs varied, but when the Mus-haf of ‘Uthmaan was written they wrote it in the order in which it appears now. Hence the order of the Mus-hafs of the Sahaabah varied… then he mentioned something similar to Ibn Battaal. End quote from Fath al-Baari. 

And Allah knows best.