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What is the next term in the sequence below?


The given sequence is:  
\[ 3, 9, 27, 81, \_\_\_\_\_, \_\_\_\_\_, \ldots \]

This is a geometric sequence where each term is multiplied by 3 to get the next term.  
Here’s how it works:

\[
9 = 3 \times 3
\]
\[
27 = 9 \times 3
\]
\[
81 = 27 \times 3
\]

Thus, the next term will be:

\[
81 \times 3 = 243
\]

And the term after that will be:

\[
243 \times 3 = 729
\]

So, the next terms in the sequence are 243 and 729. 

Would you like more details or explanations? Here are some related questions:

1. What is the general formula for the nth term in a geometric sequence?
2. How do you differentiate between arithmetic and geometric sequences?
3. Can a sequence be neither arithmetic nor geometric?
4. What happens if a geometric sequence has a ratio less than 1?
5. How does the sum of an infinite geometric series work?

**Tip**: In a geometric sequence, always check the ratio between consecutive terms to identify the pattern!

What is the next term in the sequence: 3, 9, 27, 81, ...?

Discover how to find the next terms in the geometric sequence 3, 9, 27, 81 using the formula for geometric progressions. Suitable for middle school students in Grades 6-8.

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