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The problem is about constructing and solving a recurrence relation for the salary of a B.Tech graduate, who starts with an initial salary of ₹50,000 and has a specific salary growth rule.

### Problem Breakdown:
- **Initial salary (Year 1)**: ₹50,000.
- **Salary increment rule**:
  - At the end of each year, the salary doubles compared to the previous year.
  - Additionally, there is a fixed increment of ₹10,000 for each year worked.

### Recurrence Relation Setup:
Let \( S_n \) represent her salary at the end of the \( n \)-th year. 
- **Base case**: 
  \[
  S_1 = 50,000
  \]
- **Recurrence relation**: 
  According to the problem, at the end of each year:
  - Salary doubles: \( 2S_{n-1} \)
  - Plus a fixed increment of ₹10,000 for each year worked.
  
Thus, the recurrence relation becomes:
\[
S_n = 2S_{n-1} + 10,000
\]
Where \( S_1 = 50,000 \).

### Solving the Recurrence Relation:
We now need to solve this recurrence relation to find a general formula for \( S_n \).

Let me solve this step-by-step for the salary in the \( n \)-th year.The solution to the recurrence relation is:

\[
S_n = 30,000 \cdot 2^n - 10,000
\]

This formula represents the salary at the end of the \(n\)-th year. 

- For \(n = 1\), it simplifies to the initial salary:
  \[
  S_1 = 30,000 \cdot 2^1 - 10,000 = 50,000
  \]
- For larger \(n\), you can use this formula to calculate the salary after any given year.

Do you want further details or clarifications? Here are some related questions to explore:

1. What will the salary be at the end of the 5th year?
2. How does the salary growth compare if the fixed increment was ₹15,000 instead of ₹10,000?
3. How would the salary change if the initial salary was ₹40,000 instead of ₹50,000?
4. Can the recurrence relation be solved using other methods like iteration?
5. How would the recurrence relation look if the salary increased by 150% instead of doubling?

**Tip**: You can check how rapidly the salary grows by substituting different values of \(n\) into the formula.

A freshly passed out B.Tech. Student from PDEU starts her job at a software company with a salary of Rs. 50,000 and is promised that at the end of each year her salary will be double her salary of the previous year, with an extra increment of Rs. 10,000 for each year she has been with the company. Construct and solve a recurrence relation to find her salary for her nth year of employment.

Learn how to construct and solve a recurrence relation for a salary growth problem. A B.Tech graduate starts with Rs. 50,000 salary, which doubles each year with a fixed increment of Rs. 10,000. The recurrence relation is S_n = 2S_{n-1} + 10,000. Explore the solution formula: S_n = 30,000 * 2^n - 10,000.

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