To write a recursive formula for the arithmetic sequence $\{20, 34, 48, 62, \dots\}$, we first need to identify the common difference.

Step 1: Find the Common Difference

The difference between consecutive terms is: $34 - 20 = 14, \quad 48 - 34 = 14, \quad 62 - 48 = 14$ The common difference ($d$) is $14$.

Step 2: Recursive Formula

A recursive formula for an arithmetic sequence is defined as: $a_n = a_{n-1} + d$ where $d$ is the common difference and $a_1$ is the first term.

For this sequence:

• The first term is $a_1 = 20$.
• The common difference is $d = 14$.

Thus, the recursive formula is: $a_n = a_{n-1} + 14 \quad \text{for } n \geq 2, \quad \text{with } a_1 = 20.$

Final Answer:

$\boxed{a_n = a_{n-1} + 14 \text{ for } n \geq 2, \text{ with } a_1 = 20.}$

Would you like to explore the explicit formula or graph the sequence?

---

Five Related Questions:

1. What is the explicit formula for this arithmetic sequence?
2. How can you determine the 10th term using the recursive formula?
3. What is the general formula for the $n$-th term of an arithmetic sequence?
4. How do arithmetic sequences differ from geometric sequences?
5. Can you represent this sequence visually on a graph?

Tip: When working with sequences, always double-check whether it is arithmetic or geometric by confirming the difference or ratio between terms.