Is One Intention Enough for Making up Missed Fasts Consecutively?
Question

When making up missed days from Ramadan, if my intention is to fast those days without any interruption, i.e. to fast them consecutively, is it permissible to form one intention (niyyah) to fast all of these days?
Praise be to Allah.When to form the intention for fasting
Forming the intention from the night before is a condition for every obligatory fast, according to the most correct scholarly opinion, whether that fast is being made up or is being offered on time.
The Prophet (blessings and peace of Allah be upon him): “Whoever did not intend to fast before Fajr, there is no fast for him.” (Narrated by Abu Dawud (2454), at-Tirmidhi (730) and an-Nasai (2331)
According to a version narrated by an-Nasai: “Whoever does not form the intention to fast during the night before Fajr , there is no fast for him.”
This hadith was classed as sahih by al-Albani in Sahih Abi Dawud.
Should you repeat the intention to fast every day?
The majority of jurists are of the view that it is obligatory to form the intention for each day , and it is not sufficient to form the intention (only) at the beginning of the month of Ramadan, or at the beginning of a period of consecutive fasts for all of the days.
The Malikis are of the view that one intention is sufficient for a fast that must be observed on consecutive days, such as Ramadan. As for a fast that does not have to be observed on consecutive days, such as making up missed days , it is essential to form a separate intention for each day .
It says in al-Mawsu‘ah al-Fiqhiyyah (40/275):
“The Hanafis, Shafi`is and Hanbalis are of the view that forgetting to form the intention on some nights of a fast that must be observed on consecutive days interrupts the sequence, as does omitting it deliberately, and forgetting is not regarded as a valid excuse for failing to do what is obligatory.
The Malikis are of the view that a single intention is acceptable for every fast that must be observed on consecutive days, such as Ramadan and expiatory fasts in which the fast must be observed on consecutive days.”
In al-Khulasah al-Fiqhiyyah ‘ala Madhhab as-Sadah al-Malikiyyah, it says: 
“A single intention is sufficient for every fast which must be observed on consecutive days, such as Ramadan and its expiation (i.e., the two-month expiatory fast for having intercourse during the day in Ramadan); fasts in expiation for murder or zihar (a jahili form of divorce in which a man says to his wife, ‘you are to me as my mother’s back’); and vows to observe a fast on consecutive days, as in the case of one who vows to fast a specific month… And it is essential to form the intention from the night before for each fast that may be observed on separate days, such as making up missed days of Ramadan, fasting whilst travelling, expiation for breaking an oath (kaffarat yamin), fasting in expiation for shaving the head whilst in ihram due to an ailment in the scalp, or fasting to make up for some shortcoming in performing the rituals of Hajj.”
Is one intention enough for making up missed fasts consecutively?
Based on that, if you intend to make up the Ramadan fasts on consecutive days, then you must form the intention for each day, according to the majority of scholars. I put this question to our shaykh, ‘Abd ar-Rahman al-Barrak (may Allah preserve him), and he replied:
“The intention must be formed for each day . Offering fasts to make up for missed days is not like fasting in Ramadan, according to those scholars who allow forming a single intention (for the entire month), because the days of Ramadan are consecutive as enjoined by Allah.”
However, we should point out that if someone thinks to himself that he will be fasting tomorrow, then he has formed the intention. Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: “Whoever thinks to himself that he will be fasting tomorrow has indeed formed the intention of doing so.” (Al-Ikhtiyarat al-Fiqhiyyah, in al-Fatawa al-Kubra, 4/459)
And Allah knows best.