https://file.aiquickdraw.com/mathbot/file/17289127796574xpj8o13.jpg

The problem in the image is written in Indonesian and appears to deal with salary increases over time. Here's a breakdown:

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**Problem Translation:**

A company increases its employees' salaries by a constant amount each year. If in the 3rd year the salary is IDR 3,900,000 and in the 7th year the salary is IDR 4,700,000, determine the salary received by the employee in the 5th year.

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This problem describes an arithmetic sequence, where:

- Year 3: \( a_3 = 3,900,000 \) IDR
- Year 7: \( a_7 = 4,700,000 \) IDR

In an arithmetic sequence, the general formula for the nth term is:

\[
a_n = a_1 + (n-1) \cdot d
\]

Where:
- \( a_n \) is the salary in year \( n \),
- \( a_1 \) is the initial salary (year 1),
- \( d \) is the common difference (the annual increase).

### Step 1: Find the common difference \( d \)

We know two terms in the sequence:

\[
a_7 = a_3 + (7 - 3) \cdot d
\]
\[
4,700,000 = 3,900,000 + 4d
\]

Solving for \( d \):

\[
4,700,000 - 3,900,000 = 4d
\]
\[
800,000 = 4d
\]
\[
d = 200,000
\]

Thus, the salary increases by IDR 200,000 each year.

### Step 2: Find the salary in the 5th year

Using the arithmetic sequence formula again:

\[
a_5 = a_3 + (5 - 3) \cdot d
\]
\[
a_5 = 3,900,000 + 2 \cdot 200,000
\]
\[
a_5 = 3,900,000 + 400,000 = 4,300,000
\]

Therefore, the salary in the 5th year is **IDR 4,300,000**.

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Would you like more details, or do you have any further questions? 

Here are some related questions for further exploration:

1. How do you determine the first year's salary using the given information?
2. What if the salary increase was based on a percentage rather than a fixed amount?
3. How would you find the total salary over a certain number of years?
4. What is the significance of the arithmetic sequence in salary increments?
5. How would the solution change if the salary decrease rather than increase?

**Tip:** Arithmetic sequences are useful for modeling situations where changes happen at a constant rate, such as salary increments.

Sebuah perusahaan menaikkan gaji karyawannya setiap tahun dalam jumlah yang tetap. Jika pada tahun ke-3 jumlah gaji yang diterima sebesar Rp3.900.000,00 dan pada tahun ke-7 sebesar Rp4.700.000,00, tentukan besar gaji yang diterima karyawan pada tahun ke-5.

Determine the salary of an employee in the 5th year given salary values for the 3rd and 7th years using arithmetic sequences. Learn step-by-step how to calculate salary increments.

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