Recitation in Taraweeh prayer

Firstly: 

It is better when reciting in Taraweeh to complete the
Qur’aan once. This may be understood from the reports in al-Saheehayn
which state that Jibreel used to study the Qur’aan with the Prophet
(peace and blessings of Allaah be upon him) in Ramadaan, and review it with
him. 

Shaykh Ibn Baaz said (15/325): 

It may be understood from
this that if the imam recites the entire Qur’aan to the congregation during
Ramadaan, this is a kind of this studying together, because this lets them
benefit from hearing the entire Qur’aan. Hence Imam Ahmad (may Allaah have
mercy on him) used to like to complete the Qur’aan with those whom he led in
prayer, and this is akin to what the salaf did, namely liking to hear the
entire Qur’aan. But this does not mean that he should rush and not be
deliberate in his recitation, and not seek to be focused and calm, rather
seeking these things is better than seeking to complete it. 

Majmoo’ Fataawa al-Shaykh Ibn Baaz,
11/331-333 

It says in al-Mawsoo’ah al-Fiqhiyyah (27/148): 

The Hanbalis and most of
the Hanafi shaykhs – and it was also narrated by al-Hasan from Abu Haneefah
– are of the view that the Sunnah is to complete the Qur’aan in Taraweeh
prayer so that the people can hear the entire Qur’aan in that prayer. The
Hanafis said: The Sunnah is to complete it once. So the imam should not
forsake completing it because of the people’s laziness, rather he should
recite ten verses or so in each rak’ah, and thus he will be able to complete
it. (This is based on the assumption that he prays twenty rak’ahs each
night.) And it was said that in each rak’ah thirty verses should be recited,
because ‘Umar (may Allaah be pleased with him) enjoined that. In that case
the Qur’aan can be completed three times in Ramadaan. 

Al-Kaasaani said: What ‘Umar enjoined was by way of doing
more of a good thing, which is to complete the Qur’aan more than once. This
is what was suitable for their time. But in our time it is better for the
imam to recite on the basis of the people’s situation; he should recite
whatever will not put them off from joining the congregation, because
increasing the size of the congregation is better than lengthening the
recitation. End quote. 

What al-Kaasaani said is good, and the imam should pay
attention to the situation of the people behind him. 

It is not permissible for the imam to put people off by
making the prayer so long that it becomes difficult for them and to think
that if he does not do that he has done badly! What he should do is to
encourage the people to pray even if that is by making it shorter, so long
as the prayer is complete. 

It is better for the people to offer a short but complete
prayer than not to pray at all. 

Abu Dawood said: Ahmad ibn Hanbal was asked about a man who
recited the Qur’aan twice in Ramadaan, leading the people in prayer. He
said: In my view this depends on the people’s energy level, and whether
there are workers among them. 

Ibn Rajab al-Hanbali said: The words of Imam Ahmad indicate
that attention should be paid to the state of the people with regard to
recitation; he should not make it too hard for them. This view was also
echoed by other fuqaha’ among the companions of Abu Haneefah and others. 

Lataa’if al-Ma’aarif, p. 18 

Shaykh ‘Abd al-‘Azeez ibn Baaz was asked: 

What is your opinion about what some imams do, choosing a
certain amount of Qur’aan to recite in each rak’ah each night? 

He replied: 

I do not see anything
wrong with that, because it depends on the imam’s own assessment of the
situation. If he thinks it is better to recite more on some nights and in
some rak’ahs, and that this will benefit those who are praying behind him,
and he feels that he has the energy for that and he feels that he is
enjoying the recitation and wants to recite more verses to benefit himself
and others, then he may do so. If his voice is good and he started to enjoy
the recitation and feels humble and focused and hopes that this will benefit
himself and those who are praying behind him, then if he recites some extra
verses in some rak’ahs or on some nights, we do not know of any reason why
he should not do so. The matter is broad in scope, praise be to Allaah. 

Fataawa al-Shaykh ‘Abd al-‘Azeez ibn Baaz,
11/335, 336

Shaykh ‘Abd al-‘Azeez ibn Baaz was also asked: 

Should the imam pay attention to the situation of the weak
such as the elderly etc when praying Taraweeh? 

He replied: 

This is something which is required in all the prayers, in
Taraweeh and in the obligatory prayers, because the Prophet (peace and
blessings of Allaah be upon him) said: “When any one of you leads the people
in prayer, let him make it short, because among them are the weak, the young
and those who have needs.” So the imam should pay attention to the
congregation and be kind to them with regard to praying qiyaam in Ramadaan
and during the last ten nights. People are not all the same, rather they
vary. So he should pay attention to their different situations and encourage
them to come. When he makes the prayer too lengthy, he makes it difficult
for them and puts them off from attending. He should pay attention to that
which will encourage them to attend and pray, even if that is by making it
short and not making it long. If the people concentrate during the prayer
and find peace in it only for a short time, that is better than a long
prayer in which there is no concentration and people only feel bored and
tired. 

Fataawa al-Shaykh ‘Abd al-‘Azeez ibn Baaz,
11/336, 337 

Thirdly:  

In the answer to question
no. 20043, we stated that reciting part of a soorah in prayer is
permissible, but it is better to recite the soorah in full, because this is
what the Prophet (peace and blessings of Allaah be upon him) usually
did. 

Some scholars – such as Ibn al-Salaah – made an exception in
the case of Taraweeh prayer, and said that it is better to recite part of a
soorah in them, so that (the imam) may achieve the Sunnah of completing the
Qur’aan in these prayers. 

It says in Tuhfat al-Muhtaaj Sharh al-Manhaaj (2/25): 

From this it may be
understood that if he wants to recite the whole Qur’aan in Taraweeh it is
better to recite part of the soorahs (in each rak’ah), otherwise it is
better to recite the whole soorah (in one rak’ah). End quote. 

It says in al-Mawsoo’ah al-Fiqhiyyah, 33/49: 

In one of the two reports narrated from him, Maalik regarded
it as makrooh to recite only part of a soorah, 

The Shaafa’is and Hanbalis are of the view that it is not
makrooh to recite only part of a soorah, because of the general meaning of
the verse in which Allaah says (interpretation of the meaning): 

“So, recite you of the Qur’aan as much as may be easy for
you”

[al-Muzzammil 73:20]

And Ibn ‘Abbaas (may Allaah be pleased with him) narrated
that the Prophet (peace and blessings of Allaah be upon him) used to
recite “Say (O Muslims): We believe in Allaah and that which has been
sent down to us” [al-Baqarah 2:136] in the first rak’ah of Fajr and
“Say (O Muhammad): O people of the Scripture (Jews and Christians): Come to
a word that is just between us and you” [Aal ‘Imraan 3:64] in the
second. But the Shaafa’is clearly stated that a complete soorah is better
than a passage of equivalent length from a long soorah… This applies in
prayers other than Taraweeh. But in Taraweeh reciting part of a lengthy
soorah is better. They explained that by saying that the Sunnah in Taraweeh
is to complete the whole Qur’aan in this prayer. End quote. 

In conclusion: So long as your imam is not going to complete
the Qur’aan in Taraweeh prayer, it is permissible for him to recite from
various places in the Qur’aan and that is not makrooh, although it is better
for him to recite a soorah in full. And Allaah knows best.