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

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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