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The given sequence is a geometric progression with the first three terms:

\[
81, 27, 9
\]

A geometric progression is defined by a constant ratio between consecutive terms, so we can find this ratio \(r\) by dividing the second term by the first term or the third term by the second term:

\[
r = \frac{27}{81} = \frac{1}{3}
\]

Thus, the common ratio is \(r = \frac{1}{3}\).

Now, to find the next two terms in the sequence, we continue multiplying by the common ratio \(r = \frac{1}{3}\):

1. Fourth term:
   \[
   9 \times \frac{1}{3} = 3
   \]

2. Fifth term:
   \[
   3 \times \frac{1}{3} = 1
   \]

Therefore, the next two terms of the geometric progression are:

\[
3, 1
\]

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the formula for the \(n\)-th term in a geometric progression?
2. How would the sequence change if the common ratio were negative?
3. What happens to the terms of a geometric progression as \(n\) approaches infinity if \( |r| < 1 \)?
4. How do geometric progressions apply to compound interest calculations?
5. What is the sum of the first \(n\) terms of a geometric progression?

**Tip:** When solving problems with geometric sequences, always check the common ratio by dividing successive terms to ensure consistency.

Los primeros tres términos de una sucesión geométrica son 81, 27, 9. Hallar los dos términos siguientes de esta sucesión.

Learn how to find the next two terms in a geometric progression where the first three terms are 81, 27, and 9. This problem demonstrates the concept of common ratio and geometric sequences. Suitable for students in Grades 7-9.

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