Final answer:
The Jesuit influence in China rose due to their respect for Chinese culture. However, conflicts and European intrusion led to their decline. Japan's rapid industrialization also affected China's weakened state.
Step-by-step explanation:
The rise and fall of Jesuit influence in China was influenced by various factors. Initially, the Jesuits gained respect and success in China by respecting Chinese culture, learning the language, and accommodating Chinese practices. However, conflicts with other missionary groups and the Vatican's ruling on church services and ancestral rites led to a decline in their influence. Additionally, European intrusion and conflicts weakened the Chinese government and paved the way for the rapid industrialization of Japan.