To find the next term of a geometric sequence, we need to determine the common ratio $r$, which is the constant factor by which each term is multiplied to obtain the next term.

We can calculate the common ratio by dividing any term by the previous one. Let's calculate $r$ using the first two terms:

$r = \frac{\frac{6}{5}}{-\frac{3}{5}} = -2$

Now that we know the common ratio $r = -2$, we can find the next term by multiplying the last given term $-\frac{12}{5}$ by the common ratio:

$\text{Next term} = -\frac{12}{5} \times (-2) = \frac{24}{5}$

Thus, the next term of the geometric sequence is $\frac{24}{5}$.

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Related Questions:

1. How do you find the $n$-th term of a geometric sequence?
2. What is the sum formula for an infinite geometric series?
3. How do you determine whether a sequence is geometric?
4. How can you calculate the common ratio in a geometric sequence?
5. What happens if the common ratio $r$ is a fraction or a negative number?

Tip: In a geometric sequence, if the common ratio $r$ is negative, the terms alternate in sign (positive, negative, positive, etc.).