To find the 9th term (\(a_9\)) of a geometric sequence, we can use the general formula for the \(n\)-th term of a geometric sequence:

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

where:
- \(a\) is the first term of the sequence,
- \(r\) is the common ratio, and
- \(n\) is the term number.

Given the values:
- \(a = -8\)
- \(r = 4\)
- \(n = 9\)

Let's substitute these values into the formula:

\[
a_9 = -8 \cdot 4^{(9-1)}
\]
\[
a_9 = -8 \cdot 4^8
\]

Now, we need to calculate \(4^8\):

\[
4^8 = 65536
\]

Substituting back:

\[
a_9 = -8 \cdot 65536
\]
\[
a_9 = -524288
\]

Therefore, the 9th term of the sequence (\(a_9\)) is \(-524288\).

Would you like more details or have any questions?

Here are some related questions:

1. How do you find the sum of the first \(n\) terms in a geometric sequence?
2. What is the difference between an arithmetic and a geometric sequence?
3. How do you determine if a sequence is geometric?
4. How can the common ratio of a geometric sequence affect the behavior of the sequence?
5. How do you find the nth term of a sequence if given only a few terms?

**Tip:** When working with geometric sequences, always check if the common ratio \(r\) is positive, negative, greater than 1, less than 1, or fractional, as it significantly affects the sequence's behavior.

Learn how to find the 9th term of a geometric sequence with the given values a = -8 and r = 4. Follow a step-by-step explanation using the general formula for geometric sequences. Suitable for students in Grades 9-12.

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