Find the next 3 terms of the geometric sequence if a: 12 г=½

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.

Find the next 3 terms of the geometric sequence if a: 12, r = ½

Discover how to find the next three terms of a geometric sequence where the first term is 12 and the common ratio is 1/2. This detailed solution uses the geometric sequence formula T_n = a * r^(n-1) to compute the terms, making it suitable for students in Grades 7-9.

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