The problem asks to find the common difference and the recursive formula for the sequence: $36, 34, 32, 30, \dots$.

Step 1: Finding the Common Difference

This sequence is an arithmetic sequence where the difference between consecutive terms is constant.

To find the common difference ($d$): $d = 34 - 36 = -2$ Thus, the common difference is $-2$.

Step 2: Recursive Formula

The recursive formula for an arithmetic sequence is given by: $a_n = a_{n-1} + d$ where:

• $a_n$ is the $n$-th term,
• $a_{n-1}$ is the previous term, and
• $d$ is the common difference.

Here, $a_1 = 36$ (the first term), and the common difference $d = -2$.

Thus, the recursive formula is: $a_n = a_{n-1} - 2 \quad \text{for} \quad n \geq 2, \quad \text{with} \quad a_1 = 36$

Let me know if you want more details or have any questions!

Here are 5 related questions to consider:

1. What is the general term (explicit formula) for this arithmetic sequence?
2. How would you find the 10th term of the sequence using the recursive formula?
3. What are the properties of an arithmetic sequence?
4. Can you determine the sum of the first 10 terms of this arithmetic sequence?
5. How would the recursive formula change if the common difference were positive?

Tip: Recursive formulas are great for understanding sequences step by step, but for large term calculations, an explicit formula can be more efficient!