Consider the geometric sequence {3, -6, 12, -24, ... }.  

What is the 8th term of the sequence ?

To find the 8th term of the geometric sequence, we need to use the formula for the nth term of a geometric sequence:

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

where:
- \( a_n \) is the nth term,
- \( a_1 \) is the first term,
- \( r \) is the common ratio,
- \( n \) is the term number.

### Step 1: Identify the first term \( a_1 \) and common ratio \( r \)
- The first term \( a_1 = 3 \).
- To find the common ratio \( r \), divide the second term by the first term:

\[
r = \frac{-6}{3} = -2
\]

So, the common ratio is \( r = -2 \).

### Step 2: Use the formula to find the 8th term
We want to find \( a_8 \), so substitute \( a_1 = 3 \), \( r = -2 \), and \( n = 8 \) into the formula:

\[
a_8 = 3 \cdot (-2)^{(8-1)} = 3 \cdot (-2)^7
\]

Now calculate \( (-2)^7 \):

\[
(-2)^7 = -128
\]

So:

\[
a_8 = 3 \cdot (-128) = -384
\]

### Final Answer:
The 8th term of the sequence is \( \boxed{-384} \).

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Would you like any further explanation or have any questions on the solution?

Here are some related questions:
1. What is the 5th term of this geometric sequence?
2. How do you determine the common ratio of a geometric sequence?
3. What is the sum of the first 8 terms of this geometric sequence?
4. How do geometric sequences relate to exponential functions?
5. Can you identify the general form of a geometric sequence given just the first few terms?

**Tip:** When calculating terms in a geometric sequence, remember that the common ratio \( r \) is constant between consecutive terms, and the sequence grows (or decays) exponentially based on this ratio.

Consider the geometric sequence {3, -6, 12, -24, ... }. What is the 8th term of the sequence ?

Learn how to find the 8th term of the geometric sequence {3, -6, 12, -24, ... } using the geometric sequence formula. This problem covers key concepts in exponential growth/decay and geometric sequences, making it ideal for students in Grades 7-9.

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