Write a recursive formula for the following arithmetic sequence.

 

a={17,26,35,...}

An **arithmetic sequence** is defined by a constant difference between consecutive terms. For the given sequence \( a = \{17, 26, 35, \dots\} \), the **common difference (\(d\))** is calculated as:

\[
d = a_2 - a_1 = 26 - 17 = 9
\]

The recursive formula for an arithmetic sequence is written as:

\[
a_{n} = a_{n-1} + d
\]

### Recursive Formula:
\[
a_1 = 17, \quad a_n = a_{n-1} + 9 \quad \text{for } n \geq 2
\]

This formula states that each term (\(a_n\)) is the previous term (\(a_{n-1}\)) plus the common difference \(d = 9\).

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### Do you want more details or have further questions?  
Here are 5 related questions to expand your understanding:

1. What is the explicit formula for the same arithmetic sequence?
2. How would you find the 10th term of the sequence using the recursive formula?
3. Can you derive a formula to find the sum of the first \(n\) terms of this sequence?
4. What is the difference between recursive and explicit formulas in arithmetic sequences?
5. How can you verify that a sequence is arithmetic?

**Tip:** Use the explicit formula for easier calculation of terms far into the sequence.

Write a recursive formula for the following arithmetic sequence: a = {17, 26, 35, ...}

Learn how to write a recursive formula for the arithmetic sequence a = {17, 26, 35, ...}. This step-by-step solution explains how to find the common difference and construct the recursive formula, suitable for students in Grades 6-8.

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