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we conclude that the sequence has 8 terms.
<h3>How to get the number of terms in the sequence?</h3>
Here we have the geometric sequence:
2/81, 4/27, 8/9, ..., 6912
Notice that each term is equal to 6 times the previous term, such that:
2/81*6 = 4/27
4/27*6 = 8/9
Then the n-th term is equal to:
Where in this case:
Now we need to find the value of n such that:
If we apply the natural logarithm to both sides, then:
Then we conclude that the sequence has 8 terms.
If you want to learn more about geometric sequences:
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