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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1:25 minutes

Problem 24

Textbook Question

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

Verified step by step guidance

Identify the pattern in the sequence: 74, 68, 62, ..., 38.

Notice that each term decreases by 6 from the previous term.

Determine the general form of the sequence: a_n = 74 - 6(n-1), where n is the term number.

Find the number of terms by setting the last term equal to 38: 74 - 6(n-1) = 38.

Solve for n to find the number of terms, then list all terms starting from 74 and decreasing by 6 until you reach 38.

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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 {a, b, c}. 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. This difference is known as the common difference. In the given set {74, 68, 62, ..., 38}, the common difference is -6, indicating that each term decreases by 6. Recognizing this pattern is crucial for determining all elements in the set.

Element Listing

Element listing involves explicitly writing out all the members of a set. For an arithmetic sequence, this means calculating each term until reaching the specified endpoint. In this case, starting from 74 and subtracting 6 repeatedly until reaching 38 allows for a complete enumeration of the set's elements, which is necessary for a full understanding of the set's contents.