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.