Use inductive reasoning to predict the next number in the sequence. Describe the pattern.

0, 3, 3, 0, -3, . . .

I know the next number would be -3, But what is the pattern called?

The pattern alternates between increasing by 3 and decreasing by 6. This can be described as a repeating cycle of adding 3, then subtracting 6.

The pattern in this sequence is called a "repeating pattern" or a "cyclic pattern." It alternates between the numbers 0, 3, and -3. The pattern repeats every three numbers. In a cyclic pattern, the sequence goes through a predictable cycle and continues in the same pattern indefinitely. In this case, the next number after -3 would be 0, and the sequence would continue with the pattern of 0, 3, -3, 0, 3, -3, and so on.

To find the pattern in the sequence and predict the next number using inductive reasoning, we can observe the differences between consecutive terms:

0, 3, 3, 0, -3, . . .

Notice that the first difference is 3 - 0 = 3, the second difference is 0 - 3 = -3, and the third difference is -3 - 0 = -3.

From this observation, we can see that the differences alternate between 3 and -3. This pattern suggests that the differences follow a repeating cycle of 3 and -3.

If we want to predict the next number in the sequence, we can continue this alternating pattern of differences. Since the current difference is -3, the next difference would be 3, and we would add this new difference to the last number in the sequence, which is 0. Therefore, -3 + 0 = -3, and we can conclude that the next number in the sequence is -3.

The pattern in this sequence is called an alternating pattern, where the terms or differences alternate between two distinct values (in this case, 3 and -3).