Final answer:
To find the next two terms of the sequence -16, 8, -4, 2 using inductive reasoning, we recognize the pattern where each term is the previous term multiplied by -1/2. The next terms are -1 and 0.5.
Step-by-step explanation:
Using inductive reasoning to find the next two terms of the sequence -16, 8, -4, 2, we look for a pattern in the progression of numbers. We can observe that each term is the previous term multiplied by -1/2. Applying this pattern:
- The term following 2 would be 2 × (-1/2) = -1.
- The term after -1 would be -1 × (-1/2) = 0.5.
Therefore, the next two terms of the sequence are -1 and 0.5.
To verify our pattern, we can check that each term indeed follows the multiply by -1/2 rule:
- -16 × (-1/2) = 8
- 8 × (-1/2) = -4
- -4 × (-1/2) = 2
- 2 × (-1/2) = -1
- -1 × (-1/2) = 0.5