Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:43 minutes

Problem 23

Textbook Question

Use set notation, and list all the elements of each set. {17, 22, 27, .. , 47}

Verified step by step guidance

Start by identifying the pattern in the sequence. The numbers given are 17, 22, 27, ..., 47.

Notice that each number increases by 5 from the previous number. This indicates an arithmetic sequence with a common difference of 5.

To find the elements of the set, continue adding 5 to each subsequent number starting from 17 until you reach or exceed 47.

List the elements of the set in set notation.

The set is {17, 22, 27, 32, 37, 42, 47}.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Set Notation

Set notation is a mathematical way to describe a collection of distinct objects, known as elements. It typically uses curly braces to enclose the elements, such as {1, 2, 3}. Understanding set notation is essential for identifying and listing elements within a set, as well as for performing operations like unions and intersections.

Arithmetic Sequences

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In the given set {17, 22, 27, ..., 47}, the common difference is 5. Recognizing this pattern allows one to determine all elements in the sequence and to express the set comprehensively.

Element Listing

Element listing involves explicitly writing out all the members of a set. For the arithmetic sequence mentioned, one must identify the starting point, the common difference, and the endpoint to accurately list all elements. This skill is crucial for fully representing a set in set notation.