To write a recursive formula for the given arithmetic sequence $16, 22, 28, 34, \dots$, we need the first term and the common difference.

Step 1: Identify the first term

The first term of the sequence is: $a_1 = 16$

Step 2: Find the common difference

The common difference $d$ is the difference between consecutive terms. For example: $d = 22 - 16 = 6$

Step 3: Write the recursive formula

The recursive formula for an arithmetic sequence is: $a_n = a_{n-1} + d \quad \text{for } n \geq 2$ Substituting the values: $a_n = a_{n-1} + 6 \quad \text{for } n \geq 2$

Final Answer:

$a_1 = 16$ $a_n = a_{n-1} + 6 \quad \text{for } n \geq 2$

Would you like me to explain any step further? Let me know!

Related Questions:

1. How do you derive the common difference for any arithmetic sequence?
2. What is the explicit formula for this arithmetic sequence?
3. How can you use recursion to find the 10th term of this sequence?
4. What is the general structure of an arithmetic sequence?
5. Can you write the recursive formula if the common difference is negative?

Tip: For arithmetic sequences, always identify the first term and the common difference before writing a formula!