In a geometric sequence, each term is found by multiplying the previous term by the common ratio $r$.

Given:

• First term $a = 12$
• Common ratio $r = \frac{1}{2}$

To find the next three terms, we use the formula for the $n$-th term of a geometric sequence:

$T_n = a \cdot r^{n-1}$

First term:

$T_1 = 12$

Second term:

$T_2 = 12 \times \frac{1}{2} = 6$

Third term:

$T_3 = 6 \times \frac{1}{2} = 3$

Fourth term:

$T_4 = 3 \times \frac{1}{2} = 1.5$

Thus, the next three terms of the sequence are: $6, 3, 1.5$

Would you like more details or have any questions?

Related Questions:

1. What is the sum of the first 5 terms of this geometric sequence?
2. How do you calculate the sum to infinity of a geometric series?
3. Can you find the general formula for any term in this sequence?
4. How does the value of $r$ affect the behavior of a geometric sequence?
5. How do you solve geometric sequence problems when $r$ is negative?

Tip: In a geometric sequence, if $|r| < 1$, the terms will get smaller and approach zero as the sequence progresses.