Final answer:
During John Reynolds' tenure as royal governor of Georgia, the colony did not establish the first public university, cotton plantation, state constitution, or public library.
Step-by-step explanation:
While John Reynolds was the royal governor, Georgia did not establish the first public university, the first cotton plantation, or the first state constitution. After the Georgia Trustee system collapsed in 1752, Georgia transitioned from its original status as a Trustee colony to a royal colony. During John Reynolds' tenure as royal governor, from 1754 to 1757, there were notable developments in the colony such as establishing formal governance and legal systems, but the establishment of the first public library is not historically attributed to this time period under his governance. It's important to recognize that Georgia did eventually support the development of education, as documented with the establishment of institutions like Savannah State in the 1880s and 1890s. However, this occurred long after the period of John Reynolds' governance.