To find the 8th term of a geometric sequence, we use the formula for the $n$-th term of a geometric sequence:

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

Where:

• $a_n$ is the $n$-th term.
• $a_1$ is the first term.
• $r$ is the common ratio.
• $n$ is the term position.

Step 1: Identify the given information

• The 3rd term ($a_3$) is 27.
• The common ratio ($r$) is 3.

Step 2: Find the first term ($a_1$)

The formula for the 3rd term is: $a_3 = a_1 \cdot r^{3-1}$

Substitute $a_3 = 27$ and $r = 3$: $27 = a_1 \cdot 3^2$

Simplify: $27 = a_1 \cdot 9$

Solve for $a_1$: $a_1 = \frac{27}{9} = 3$

Step 3: Find the 8th term ($a_8$)

Now use the formula for the 8th term: $a_8 = a_1 \cdot r^{8-1}$

Substitute $a_1 = 3$, $r = 3$, and $n = 8$: $a_8 = 3 \cdot 3^{7}$

Simplify: $a_8 = 3 \cdot 2187 = 6561$

Final Answer:

The 8th term of the sequence is: $\boxed{6561}$

Would you like further details or explanations?

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Related Questions:

1. What is the formula for the sum of the first $n$ terms in a geometric sequence?
2. How does the common ratio affect the growth of a geometric sequence?
3. What is the 10th term of this sequence?
4. How do you determine if a sequence is arithmetic or geometric?
5. Can you derive the general term formula for a geometric sequence?

Tip: When working with geometric sequences, always verify the common ratio and calculate step-by-step to avoid compounding errors.