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Encuentra el término que se pide en la siguiente progresión geométrica: 

567
189
63
21

You are asked to find the 4th term, \( a_4 \), in the given geometric progression with the formula \( a_n = 7 \times (3^{n-1}) \).

### Step-by-Step Solution:

1. **Identify the formula**: 
   \[
   a_n = 7 \times (3^{n-1})
   \]
   
2. **Substitute \( n = 4 \) into the formula**:
   \[
   a_4 = 7 \times (3^{4-1}) = 7 \times (3^3)
   \]
   
3. **Calculate \( 3^3 \)**:
   \[
   3^3 = 27
   \]
   
4. **Multiply the result by 7**:
   \[
   a_4 = 7 \times 27 = 189
   \]

### Final Answer:
The 4th term of the progression, \( a_4 \), is \( \boxed{189} \).

Would you like more details, or do you have any questions?

Here are 5 related questions for practice:
1. What is the 5th term of the sequence given by \( a_n = 7 \times (3^{n-1}) \)?
2. How do you find the sum of the first 5 terms of this geometric progression?
3. What is the common ratio of the sequence?
4. How would the formula change if the first term were 14 instead of 7?
5. How would you find the 10th term in this sequence?

**Tip:** In geometric sequences, identifying the common ratio helps in predicting future terms efficiently.

Learn how to find the 4th term in a geometric progression using the formula a_n = 7 * (3^(n-1)). Follow a detailed step-by-step solution to solve the problem. Suitable for students in Grades 7-9.

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