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The sequence \(6075, 2025, 675 \ldots\), is made by repeatedly dividing by 3. How many integers are in this sequence?

 Aug 6, 2020
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Here is one of the many ways you can approach this problem:

 

As you see, there is a pattern: eachtime, you are taking away a digit, starting from 0.

So, we have

6075, 2025, 675, 225, 75, 25 (see the pattern? the last 2 digits are always the same)

Using this pattern, we see that for the last 2 digits to remain the same, it cannot go any further without becoming a fraction. So, there are a total of 6 integers.

 Aug 6, 2020

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