Identify a pattern in the given list of numbers. Then use this pattern to find the next number.​ (More than one pattern might​ exist, so it is possible that there is more than one correct​ answer.)
3, 9, 27, 81, 243

The sequence given is:

\[ 3, 9, 27, 81, 243 \]

To identify a pattern, let's examine the relationship between consecutive terms:

1. **First Term to Second Term**: \( 9 \div 3 = 3 \)
2. **Second Term to Third Term**: \( 27 \div 9 = 3 \)
3. **Third Term to Fourth Term**: \( 81 \div 27 = 3 \)
4. **Fourth Term to Fifth Term**: \( 243 \div 81 = 3 \)

Each term is obtained by multiplying the previous term by 3. Therefore, the pattern is a geometric sequence with a common ratio of 3.

To find the next number in the sequence:

\[ 243 \times 3 = 729 \]

So, the next number in the sequence is **729**.

Would you like a detailed explanation of geometric sequences or have any questions?

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Here are 5 relative questions to consider:

1. What would be the 8th term in this sequence?
2. How can the general formula for the \(n\)th term of a geometric sequence be derived?
3. What is the sum of the first 5 terms of this sequence?
4. How does changing the common ratio affect the sequence?
5. Can you identify a different pattern in the sequence that gives a different next term?

**Tip:** In geometric sequences, each term is a constant multiple of the previous term, which makes them predictable and easy to calculate for large \(n\).

Understand the pattern in the sequence 3, 9, 27, 81, 243 and learn how to find the next number using the common ratio of a geometric sequence. This problem explores geometric sequences and the nth term formula, suitable for Grades 7-9.

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