The problem involves identifying the salary in the sixth year of employment based on the provided salary sequence:
$50,000; 50,700; 51,400; 52,100; 52,800.$

We need to determine the pattern and predict the sixth year's salary.

Step 1: Analyze the pattern

The sequence shows an incremental increase:

• From year 1 to 2: $50,700 - 50,000 = 700$
• From year 2 to 3: $51,400 - 50,700 = 700$
• From year 3 to 4: $52,100 - 51,400 = 700$
• From year 4 to 5: $52,800 - 52,100 = 700$

The salary increases by $700 each year.

Step 2: Predict year 6 salary

To find the sixth-year salary, add $700 to the fifth-year salary: $52,800 + 700 = 53,500.$

Final Answer:

$53,500

Would you like a step-by-step explanation of the logic used here or details about salary progression?

5 Related Questions:

1. What would the salary be in the 10th year at this rate of increase?
2. How would the solution change if the yearly increase doubled?
3. Can this salary pattern be modeled using a linear equation?
4. What is the total salary earned over the first six years?
5. How does the constant increase affect long-term earning potential?

Tip:

When analyzing patterns, always check the differences between consecutive terms first—it often reveals the trend quickly.