Final answer:
The primary purpose of the mid-16th-century series of meetings was to reinvigorate and strengthen the Catholic Church following the Protestant Reformation. This series of meetings is known as the Council of Trent.
Step-by-step explanation:
The series of meetings in the mid-16th century that aimed to reinvigorate and strengthen the Catholic Church following the Protestant Reformation is known as the Council of Trent. This council was held in Trent, Northern Italy, for 25 sessions over a period of 18 years, starting in 1545. During the Council of Trent, the Church addressed the challenges raised by Martin Luther and affirmed the Doctrine of Merit, the importance of sacraments, the existence of Purgatory, the authority of scripture and teachings of the Church, and the necessity of religious art.