Final answer:
The execution of the king during the French Revolution was caused by the revolutionaries' push for a republican government, the radicalization of the revolution leading to the period of the Terror, and the king and queen's attempted escape.
Step-by-step explanation:
The events that led to the execution of the king during the French Revolution can be attributed to several factors. Firstly, the revolutionaries advocated for a direct representative democracy and saw the monarchy as an obstacle to their goals of establishing a republican government. Secondly, the execution was fueled by the radicalization of the revolution, which resulted in a period known as the Terror. This period of extreme violence against perceived enemies led to the execution of King Louis XVI as well as many other aristocrats believed to be loyal to the monarchy. Finally, the attempt by the king and queen to escape across the border to the Austrian Empire further fueled the revolutionaries' desire to eliminate the monarchy.