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