Use set notation, and list all the elements of each set. {74, 68, 62, ..., 38}

Verified step by step guidance

1. Identify the pattern in the given set: {74, 68, 62, ..., 38}. Notice that the numbers are decreasing by 6 each time (74 to 68 is -6, 68 to 62 is -6).
2. Determine the rule for the sequence. Since the numbers decrease by 6, the sequence can be described as starting at 74 and subtracting 6 repeatedly until reaching 38.
3. List all the elements by continuing the pattern: 74, 68, 62, 56, 50, 44, 38.
4. Write the set in set notation by listing all elements explicitly: {74, 68, 62, 56, 50, 44, 38}.
5. Verify that the last element matches the given endpoint (38) and that all elements follow the pattern of decreasing by 6.

Key Concepts

Set Notation

Set notation is a way to describe a collection of elements using curly braces {}. Elements can be listed explicitly or described by a rule. For example, {1, 2, 3} lists elements, while {x | x is an even number less than 10} uses a rule.

Arithmetic Sequences

An arithmetic sequence is a list of numbers with a constant difference between consecutive terms. For example, in the sequence 74, 68, 62, ..., the difference is -6. Understanding this helps identify all elements in the set.

Listing Elements of a Sequence

To list all elements of a sequence, start from the first term and repeatedly add the common difference until reaching the last term. This process ensures all elements are included and correctly ordered.