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The problem provided discusses the production of cigarettes by a factory. Let's break down and solve it step by step.

### Given Data:
1. **Initial production in year 1**: 1,000,000 packs.
2. **Production in year 6**: 1,750,000 packs.
   
We assume the production increases at a constant rate each year.

### a. Find the additional production per year:
The increase in production from year 1 to year 6 is linear, meaning the same amount is added every year. To find the annual increase, we can use the formula for the slope between two points in arithmetic sequences:

\[
\text{Increase per year} = \frac{\text{Production in year 6} - \text{Production in year 1}}{6 - 1}
\]

Let's calculate this.

\[
\text{Increase per year} = \frac{1,750,000 - 1,000,000}{6 - 1} = \frac{750,000}{5} = 150,000
\]

So, the production increases by 150,000 packs per year.

### b. Find the production in year 11:
Since the production increases by 150,000 packs per year, we can calculate the production in year 11 by extending the arithmetic sequence.

The formula for the \(n\)-th term of an arithmetic sequence is:

\[
P_n = P_1 + (n - 1) \times d
\]

Where:
- \(P_n\) is the production in year \(n\),
- \(P_1\) is the production in year 1 (1,000,000 packs),
- \(d\) is the increase per year (150,000),
- \(n = 11\).

Substituting the values:

\[
P_{11} = 1,000,000 + (11 - 1) \times 150,000
\]
\[
P_{11} = 1,000,000 + 10 \times 150,000
\]
\[
P_{11} = 1,000,000 + 1,500,000 = 2,500,000
\]

Thus, the production in year 11 will be 2,500,000 packs.

### Summary:
- The additional production per year is **150,000** packs.
- The production in year 11 will be **2,500,000** packs.

Would you like more details on any step or further clarification? Here are some related questions for you:

1. What if the production increased by a different amount every year instead of a constant rate?
2. How would we calculate the production in year 20?
3. Can we model this problem using a different method like geometric sequences?
4. What if the production in year 1 had been lower—how would that change the result?
5. Can this method apply to other real-world problems, such as factory output for different products?

**Tip**: Always verify if the given pattern (constant increase) holds in similar real-world scenarios before making predictions.

Sebuah pabrik rokok 'Sampurna' menghasilkan 1.000.000 bungkus rokok pada tahun pertama, dan 1.750.000 bungkus pada tahun ke-6. a. Andaikan produksinya konstan, berapa tambahan produksinya per tahun? b. Berapa besar produksi rokoknya pada tahun ke-11?

Learn how to calculate the growth in cigarette production in a factory using arithmetic progression. Starting from 1,000,000 packs in year 1, production increased to 1,750,000 packs by year 6. This problem walks you through finding the annual increase and predicting production for year 11. Suitable for Grades 9-10.

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