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.