Example $2$:Determining the Number of Terms

Carpenter ants are large, usually black ants that make their colonies in wood. Although often considered to be pests around the home, carpenter ants play a significant role in a forested ecosystem $.$ Sarpenter ants begin with a parent colony. When this colony is well$-$established, they form satellite colonies consisting of only the workers. An established colony may have as many as $3000$ ants. Suppose that the growth of the colony produces an arithmetic sequence in which the number of ants increases by approximately $80$ ants each month. Beginning with $40$ ants, how many months would it take for the ant population to reach $3000?$