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The problem discusses Mr. Anton, a duck farmer who collects eggs, with the number of eggs forming an arithmetic sequence. We are given the following information:

- Mr. Anton collects a total of **9,000 eggs** over **3 months** (90 days, since \( 1 \text{ month} = 30 \text{ days} \)).
- On the **first day**, he collects **30 eggs**.
- We are asked to find how many eggs he collects on the **last day**.

### Step-by-Step Solution:

1. **Identify the Arithmetic Sequence**:
   - The total number of days is \( n = 90 \) (since 3 months = 90 days).
   - The first term of the sequence is \( a = 30 \) (he collects 30 eggs on the first day).
   - Let the number of eggs collected on the last day (day 90) be \( l \), which is the value we need to find.

2. **Sum of the Arithmetic Sequence**:
   The sum \( S \) of an arithmetic sequence is given by the formula:
   \[
   S = \frac{n}{2} \times (a + l)
   \]
   Where:
   - \( S = 9,000 \) (the total number of eggs),
   - \( n = 90 \),
   - \( a = 30 \),
   - \( l \) is the number of eggs on the last day.

   Substituting the values we know:
   \[
   9000 = \frac{90}{2} \times (30 + l)
   \]
   Simplifying:
   \[
   9000 = 45 \times (30 + l)
   \]
   \[
   9000 = 1350 + 45l
   \]
   Solving for \( l \):
   \[
   9000 - 1350 = 45l
   \]
   \[
   7650 = 45l
   \]
   \[
   l = \frac{7650}{45} = 170
   \]

Thus, the number of eggs collected on the last day is **170 eggs**.

### Final Answer:
Mr. Anton collects **170 eggs** on the last day.

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Would you like further explanation or details on any part of the solution?

Here are 5 related questions to expand on this concept:
1. How would the answer change if Mr. Anton collected 40 eggs on the first day instead of 30?
2. How would you determine the common difference in this arithmetic sequence?
3. Can you calculate the total number of eggs collected after the first 45 days?
4. What would be the sum if the total period was 120 days instead of 90 days?
5. How do arithmetic sequences relate to geometric sequences in terms of growth patterns?

**Tip:** Always remember that the sum of an arithmetic sequence is directly influenced by the number of terms and the average of the first and last terms.

Pak Anton seorang peternak bebek. Ia mengumpulkan telur bebek sebanyak 9.000 butir selama 3 bulan. Banyak telur yang Pak Anton kumpulkan setiap hari nya membentuk barisan aritmetika. Pada hari pertama ia mengumpulkan telur bebek sebanyak 30 butir. Telur yang Pak Anton kumpulkan pada hari terakhir adalah …. (1 bulan = 30 hari).

Learn how to solve a problem involving Pak Anton, a duck farmer, who collects 9,000 eggs over 90 days, forming an arithmetic sequence. The solution includes detailed steps to find the number of eggs collected on the last day. Suitable for Grades 9-11.

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