This equation describes a recurrence relation, where each value \( y_n \) depends on the previous value \( y_{n-1} \). It follows this pattern:

\[
y_n = y_{n-1} \cdot 1.005 + 200
\]

This kind of recurrence relation is commonly used to model processes like compound interest with additional regular deposits. Here's a step-by-step breakdown of the relation:

1. **Start Value:** You need an initial value for \( y_0 \) (or another starting point, such as \( y_1 \)).
2. **Growth Factor:** Each term grows by multiplying the previous term by 1.005 (a 0.5% increase).
3. **Constant Addition:** After applying the growth factor, 200 is added to the result.

### Example Calculation:
Let's say you start with \( y_0 = 1000 \).

- \( y_1 = 1000 \cdot 1.005 + 200 = 1005 + 200 = 1205 \)
- \( y_2 = 1205 \cdot 1.005 + 200 = 1211.025 + 200 = 1411.025 \)

This pattern continues for further values of \( y_n \).

Would you like to calculate more values, or explore specific applications of this recurrence relation?

Here are 5 related questions:
1. What happens to \( y_n \) as \( n \to \infty \)?
2. How would changing the 200 constant affect the growth pattern?
3. Can you express this recurrence relation in a closed form?
4. How would the relation change if the growth rate were 1.01 instead of 1.005?
5. Could this model be applied to a financial saving plan with regular deposits?

**Tip:** Recurrence relations are widely used to model sequences in finance, population growth, and algorithm analysis!

Understand the recurrence relation equation yn = yn-1 * 1.005 + 200 with detailed explanations of growth patterns and constant additions. This mathematical model is ideal for modeling processes like compound interest with additional deposits. Suitable for students in Grades 10-12.

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