SOLUTION: # 1. Use inductive reasoning to determine the next three numbers in the pattern: 1, 1/3, 1/9, 1/27, ...

Question 190609: # 1. Use inductive reasoning to determine the next three numbers in the pattern: 1, 1/3, 1/9, 1/27, ...
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1
Q: Use inductive reasoning to determine the next three numbers in the pattern: 1, 1/3, 1/9, 1/27, ...

A:

From the first term 1 to the second term , notice how the second term is just the first term divided by 3. So let's see if this holds from the second term to the third term.

If we divide by , we get:

So this shows that if we divide by , we get

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Now let's divide , by to get:

So dividing by gets us

So using inductive reasoning, we would conjecture that this pattern continues indefinitely.

So this means that we can find the next three terms by dividing each previous term by 3.

So divide by 3 to get

So the next term is

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Now divide by 3 to get

So the next term is
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So divide by 3 to get

So the next term is

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Answer:

So the next three terms of the sequence are , , and

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