To find the next term in a geometric sequence, we first need to identify the common ratio, which is the constant factor between consecutive terms.

In the given sequence: $189, 63, 21, \dots$

Let's calculate the common ratio $r$:

$r = \frac{63}{189} = \frac{1}{3}$ $r = \frac{21}{63} = \frac{1}{3}$

So, the common ratio $r = \frac{1}{3}$.

Now, to find the next term, we multiply the last term (21) by the common ratio $\frac{1}{3}$:

$\text{Next term} = 21 \times \frac{1}{3} = 7$

Thus, the next term in the sequence is $\boxed{7}$.

Would you like further explanation on this, or have any questions?

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Here are 5 related questions:

1. How do you determine the common ratio of a geometric sequence?
2. What is the formula for the nth term of a geometric sequence?
3. How do you calculate the sum of the first $n$ terms of a geometric sequence?
4. What happens if the common ratio in a geometric sequence is negative?
5. How do you find the nth term if the first term is given and the common ratio is known?

Tip: When working with geometric sequences, always confirm that the ratio between consecutive terms is constant before assuming the pattern will continue.