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!