Final answer:
Using inductive reasoning on the sequence 1, 8, 27, 64, 125, the next term is 216 since the sequence represents the cubes of consecutive natural numbers. it's evident that the numbers are the cubes of consecutive natural numbers (1^3, 2^3, 3^3, 4^3, and 5^3 respectively). Thus, the next term in the sequence would logically be 6^3, which is 216.
Step-by-step explanation:
The subject of the student's question is to use inductive reasoning to predict the next term of the sequence 1, 8, 27, 64, 125. Upon evaluating the sequence, it's evident that the numbers are the cubes of consecutive natural numbers (1^3, 2^3, 3^3, 4^3, and 5^3 respectively). Thus, the next term in the sequence would logically be 6^3, which is 216.
Inductive reasoning, or inductive logic, is a type of reasoning that involves drawing a general conclusion from a set of specific observations. Some people think of inductive reasoning as “bottom-up” logic, because it involves widening specific premises out into broader generalizations.Here is a basic form of inductive reasoning, with a premise based on concrete data and a generalized conclusion:1. All the swans I have seen are white. (Premise)2. Therefore all swans are white. (Conclusion)In this example, the conclusion is actually wrong—there are also black swans. This is what’s called a “weak” argument. However, it’s easy to make the conclusion stronger, by making it more probable:1. All the swans I have seen are white. (Premise)2. Therefore most swans are probably white. (Conclusion)