It is legislated to let those being led in Prayer hear all of the Qur'an in order in the Tarawih Prayer

Question :

If I am an Imam in the Tarawih prayer, am I obligated to recite every night Verses that follow in succession that It has been confirmed in the Sahih that which preceded them. Meaning, do I recite the Suraks of the Qur'an in successive order or do I read from where I stopped from the Verses that I recited during the day?

Answer:

What is legislated for the Imams is that they allow those being led in prayer to hear all of the Qur'an during the night prayer of Ramadhan if they are able to do so. Thus, the Imam should recite Verses and Surahs every night that come after what he recited in the previous night so that those praying behind him hear all of the Book of their Lord in succession according to its arrangement in the Qur'an. If he is able to complete the entire Qur'an with them to the end, then that is better if it is not difficult on them. He should do this giving attention to slow rhythmic recitation, humility and tranquility. This is because the intent of the prayer is nearness to Allâh and humbleness before Him, hoping for what is with Him of reward and being fearful of what is with Him of punishment. The intent is not simply to offer Rak'ahs without any humility or attention of the heart before Allâh, glory is unto Him the Most High. May Allah help the Muslims in that which contains their rectification and salvation in this life and the Hereafter.

Source:
Ash-Shaykh Ibn Baz
Fatawa Islamiyah, Vol. 3 Pages 320-321