Question
Asked Sep 14, 2019
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How can I use Inductive Reasoning to predict the next three numbers after 9, -45/4 , 225/16 , -1125/64

mathmatics for liberal arts 1

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Expert Answer

Step 1

Notice that the numerator of numbers can be written as:

       9 = (-5)0 × 9
    -45 = (-5)1 × 9
   225 = (-5)2 × 9
-1125 = (-5)3 × 9

Taking this trend therefore the next three numbers in this sequence would be:
(-5)4 × 9 = 5625
(-5)5 × 9 = -28125
(-5)6 × 9 = 140625


Step 2

Notice that the denominator of numbers can be written as:

  1 = (4)0   
  4 = (4)1     
16 = (4)2
64 = (4)3   

Taking this trend therefore the next three numbers in this sequence would be:
(4)4  ...

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