Final answer:
The availability of fertile soil for agriculture, propelled by the Homestead Act of 1862 and the development of infrastructure such as the Transcontinental Railroad, was the main reason for the rapid settlement of the Great Plains in the late eighteenth century.
Step-by-step explanation:
The main reason for the rapid settlement of the Great Plains during the late eighteenth century was the availability of fertile soil for agriculture, as encouraged by government incentives like the Homestead Act of 1862. This act offered 160 acres of free land to households willing to move and settle in the west. Furthermore, the completion of the Transcontinental Railroad in 1869 and various pieces of legislation facilitated this movement, while forts built by the U.S. government, such as Fort Laramie and Fort Apache, provided aid and support to settlers. Despite challenges, including the need for financial resources to undertake the move and the hard work required to cultivate the land, the possibility of owning property and leading a more independent lifestyle drove many to migrate westward.