Make a real life problem with sum of geometric sequence with small numbers 

### Problem: 

Maria is planting a row of flowers in her garden. She starts by planting 2 flowers in the first section of the row. She wants to plant more flowers in each subsequent section, so she decides to double the number of flowers in each following section. She plans to plant flowers in 5 sections in total.

How many flowers will Maria plant in total?

### Solution:

The number of flowers in each section forms a geometric sequence where:

- The first term \( a_1 = 2 \) (flowers in the first section).
- The common ratio \( r = 2 \) (each section has double the number of flowers as the previous one).
- The number of terms \( n = 5 \) (sections).

The sum of the first \( n \) terms of a geometric sequence can be calculated using the formula:

\[
S_n = \frac{a_1(1 - r^n)}{1 - r}
\]

Plugging in the values:

\[
S_5 = \frac{2(1 - 2^5)}{1 - 2} = \frac{2(1 - 32)}{-1} = \frac{2(-31)}{-1} = 62
\]

So, Maria will plant a total of 62 flowers.

Would you like more details or have any questions?

### Related Questions:
1. What if Maria decided to triple the number of flowers instead of doubling them?
2. How many flowers would she have planted if she had only 3 sections?
3. What is the sum of flowers if the sequence continued for 6 sections?
4. Can you find the number of flowers in each section individually?
5. How would the total change if she started with 4 flowers instead of 2?

### Tip:
When dealing with geometric sequences, remember that the common ratio greatly influences how quickly the sequence grows.

Explore how to calculate the total number of flowers Maria will plant in her garden using a geometric sequence. Learn about geometric sequences, exponential growth, and the sum of a geometric series formula. Suitable for Grades 6-8.

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