The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).
3, comma, 9, comma, 27, comma, point, point, .
3,9,27,...
Find the 7th term.
Find the 7th term.

The given sequence is: 3, 9, 27, ...

This is a geometric sequence, where each term is multiplied by a constant ratio to get the next term. Let's calculate the common ratio \( r \).

\[
r = \frac{\text{second term}}{\text{first term}} = \frac{9}{3} = 3
\]

Now that we know the common ratio \( r = 3 \), we can use the formula for the \(n\)-th term of a geometric sequence:

\[
a_n = a_1 \cdot r^{n-1}
\]

where:
- \(a_1 = 3\) (the first term),
- \(r = 3\),
- \(n = 7\) (we are looking for the 7th term).

Now, calculate the 7th term:

\[
a_7 = 3 \cdot 3^{7-1} = 3 \cdot 3^6 = 3 \cdot 729 = 2187
\]

So, the 7th term is:

\[
\boxed{2187}
\]

Would you like more details on geometric sequences or have any other questions?

Here are 5 related questions to think about:
1. What is the formula for the sum of the first \(n\) terms of a geometric sequence?
2. How would the formula for the \(n\)-th term change if the ratio were negative?
3. How can you recognize if a sequence is arithmetic instead of geometric?
4. If the common ratio were a fraction, how would that affect the terms of the sequence?
5. What happens to the sequence if the first term is negative?

**Tip:** Always check if the sequence follows a constant ratio to determine if it’s geometric!

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary). 3,9,27,... Find the 7th term.

Learn how to find the 7th term in the geometric sequence 3, 9, 27,... using the geometric sequence formula. This detailed solution covers exponential growth and calculating terms in geometric sequences. Suitable for students in Grades 9-11.

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