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Use inductive reasoning to find the next two terms of each sequence: -16, 8, -4, 2...

User James Tan
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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
User Chintan Parmar
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