Juan examines the sequence 1, 3, 4, 7, 11, . . . and draws the conclusion that the next number in the sequence is 18. Which statements regarding the situation are accurate? Check all that apply.Juan used inductive reasoning.Juan's conclusion is a conjecture.Juan's conclusion is not possible.Juan's conclusion is a counterexample. Juan based his conclusion on patterns.
Answer
A
Juan used inductive reasoning.
B
Juan's conclusion is a conjecture.
C
Juan's conclusion is not possible.
D
Juan's conclusion is a counterexample.
E
Juan based his conclusion on patterns.
Explanation
Juan noticed a pattern: each term is the sum of the two terms before it (1 + 3 = 4, 3 + 4 = 7, and 4 + 7 = 11). Continuing that pattern gives 7 + 11 = 18. Reasoning from observed examples to a likely next term is inductive reasoning, and the conclusion is a conjecture based on patterns—not a counterexample or an impossible result.
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