rewrite the following set by listing their elements between braces. If it is an infinite set, write out enough elements to see the pattern, then use ellipses. {5n + 3}: n e z

The set \(\{5n + 3 : n \in \mathbb{Z}\}\) can be written by listing the elements as follows:

\[
\{ \dots, -7, -2, 3, 8, 13, 18, \dots \}
\]

This is an infinite set that includes all integers of the form \(5n + 3\), where \(n\) is any integer.

Would you like more details on how this set was constructed?

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Here are 5 related questions:
1. What is the pattern of the differences between consecutive terms in the set?
2. How would the set change if the formula were \(5n - 2\)?
3. Can you express the general term for a set formed by \(an + b\) for any \(a\) and \(b\)?
4. What would the set look like if \(n\) were restricted to non-negative integers?
5. How does this set relate to modular arithmetic?

**Tip**: Understanding the arithmetic progression in sets like this can help solve equations involving linear patterns.

Rewrite the following set by listing their elements between braces. If it is an infinite set, write out enough elements to see the pattern, then use ellipses. {5n + 3}: n ∈ Z

Explore how to list the elements of the arithmetic sequence defined by {5n + 3}, where n belongs to the set of integers. This problem introduces the concept of arithmetic sequences and integer sets. Suitable for students in Grades 9-12.

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