Question

The first four numbers in a sequence are 1, 4, 9, and 16.

Patrice determines the next number is 25. What type of reasoning did he use to determine this number?
a. inductive
b. deductive
c. both inductive and deductive
d. neither inductive or deductive

Answer 1

Patrice used inductive reasoning to determine the next number in the sequence.

Step-by-step explanation:

The type of reasoning that Patrice used to determine the next number in the sequence is inductive reasoning. Inductive reasoning is a logical thinking process that uses related observations to arrive at a general conclusion. In this case, Patrice observed that the sequence is increasing by adding the square of the next natural number, such as 12 (1), 22 (4), 32 (9), and 42 (16), so it is reasonable to conclude that the next number would be 52 (25).