Question

Use Inductive reasoning to describe each pattern and

and find the next two terms of
-16, 8, -4, 2...

Answer 1

The pattern in the given sequence is an alternation of positive and negative differences. By observing the differences between consecutive terms, we can find the next two terms.

Step-by-step explanation:

The given sequence is -16, 8, -4, 2...

To find the pattern and the next two terms, we need to look for the difference between consecutive terms. Let's calculate the difference between each pair of terms:

• 8 - (-16) = 24
• -4 - 8 = -12
• 2 - (-4) = 6

Now, we can observe that the differences alternate between positive and negative values. Specifically, the differences are positive, negative, positive, and so on. Therefore, the pattern can be described as follows: Starting with a negative value (-16), the next term is obtained by adding a positive difference (24) to the previous term, and then the subsequent term is obtained by subtracting a negative difference (12) from the previous term.

Applying this pattern, we can find the next term and the term after that:

• 2 + 6 = 8
• 8 - 12 = -4