Make a word problem of sum of the geometric sequence

Here's a word problem involving the sum of a geometric sequence:

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**Problem:**  
A farmer is planting trees in a row, starting with 3 trees in the first row. Each subsequent row has twice as many trees as the previous row. If the farmer plants 6 rows of trees, how many trees are there in total?

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**Explanation:**  
The number of trees in each row forms a geometric sequence where:

- The first term \( a = 3 \) (the number of trees in the first row).
- The common ratio \( r = 2 \) (since each row has twice as many trees as the previous one).
- The total number of rows \( n = 6 \).

To find the total number of trees, we need the sum of the first 6 terms of the geometric sequence.

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Would you like me to provide the detailed steps to solve this?  
Here are 5 questions related to this concept:

1. How do you find the sum of a geometric sequence?
2. What happens if the common ratio of a geometric sequence is less than 1?
3. Can you have a geometric sequence with a negative common ratio?
4. How is the geometric sequence used in finance or economics?
5. What would happen if the common ratio were 3 instead of 2 in this problem?

**Tip:** When working with geometric sequences, always ensure that the common ratio \( r \) is consistent between terms.

Explore this word problem about summing a geometric sequence. A farmer plants 6 rows of trees, with each row having twice as many trees as the previous one. Learn how to calculate the total number of trees using the sum of a geometric sequence. Suitable for students in Grades 9-10.

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