Write a recursive formula for the arithmetic sequence.

 

{20,34,48,62,…}

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? 

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**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.

Write a recursive formula for the arithmetic sequence {20, 34, 48, 62, …}.

Discover how to write a recursive formula for the arithmetic sequence {20, 34, 48, 62, …}. This solution explains the concept of common difference, the recursive formula structure, and provides a step-by-step derivation suitable for Grades 8-10.

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