Make a word problem of sum of geometric sequence 

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

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**Word Problem:**

Emma is training for a marathon. She decides to start by running 2 kilometers on the first day. Each day after that, she doubles the distance she runs compared to the previous day. Emma plans to run like this for 7 days.

**Question:**  
What is the total distance Emma will have run by the end of the 7th day?

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To solve this, we recognize that the distances form a geometric sequence:
- First term (a) = 2 km
- Common ratio (r) = 2 (since she doubles the distance each day)
- Number of terms (n) = 7

The formula for the sum \(S_n\) of the first \(n\) terms of a geometric sequence is:

\[
S_n = a \times \frac{(r^n - 1)}{r - 1}
\]

Let me know if you'd like to see the solution or have any questions!

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**Relative Questions:**
1. What would happen if Emma tripled the distance each day instead of doubling it?
2. How much distance would Emma have run if she continued her plan for 10 days?
3. If Emma started by running 3 km on the first day, how would this affect the total distance after 7 days?
4. What would the total distance be if Emma halved the distance she runs every day instead of doubling it?
5. How does the common ratio affect the total sum in a geometric sequence?

**Tip:** In geometric sequences, the common ratio significantly affects how quickly the sequence grows or shrinks.

Make a word problem of sum of geometric sequence.

Explore a real-world example of the sum of a geometric sequence in this word problem about marathon training. Learn how to calculate the total distance run over 7 days with a step-by-step breakdown using the geometric series formula. Ideal for students in Grades 9-11.

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