Why Do We Say Arithmetic Sequence? (Solved)

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence. That is how the terms in the sequence are generated.

Why do you think it is called an arithmetic sequence?

Sequences with such patterns are called arithmetic sequences. In an arithmetic sequence, the difference between consecutive terms is always the same. The sequence 21, 16, 11, 6 is arithmetic as well because the difference between consecutive terms is always minus five.

What is an arithmetic sequence meaning?

An arithmetic sequence is a sequence of numbers which increases or decreases by a constant amount each term. Once you know the common difference, you can find the value of c by plugging in 1 for n and the first term in the sequence for a1. Example 1: {1,5,9,13,17,21,25,}

What did you learn about arithmetic sequence?

We’ve learned that arithmetic sequences are strings of numbers where each number is the previous number plus a constant. The common difference is the difference between the numbers. If we add up a few or all of the numbers in our sequence, then we have what is called an arithmetic series.

How did you understand arithmetic?

Arithmetic is working with the numbers themselves. This includes counting, adding, subtracting, multiplying, and dividing. It also includes fractions, positive and negative numbers, the order of operations, sequencing, and more. Basically, arithmetic math is how the numbers work together to get an answer to a problem.

What is the meaning of arithmetic mean?

The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series. For example, take the numbers 34, 44, 56, and 78.

How do you use the arithmetic sequence?

Solution: To find a specific term of an arithmetic sequence, we use the formula for finding the nth term. Step 1: The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

Why do we need to study arithmetic series?

The arithmetic sequence is important in real life because this enables us to understand things with the use of patterns. An arithmetic sequence is a great foundation in describing several things like time which has a common difference of 1 hour. An arithmetic sequence is also important in simulating systematic events.

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This is the third edition of the book, which has been updated. The previous edition is available on the site for the second edition. Discrete Mathematics: An Open Introduction is a free, open source textbook that may be used for a first or second year undergraduate course in discrete mathematics for math majors, particularly those who plan to go on to become teachers in the future. The book has been utilized as either the major textbook or a supplemental resource at more than 75 colleges and institutions throughout the world since its publication in Spring 2013.

The material has been endorsed by the Open Textbook Initiative of the American Institute of Mathematics and has received positive reviews on the Open Textbook Library.

All previously published editions will remain on the market forever.

For further information, please see theerrata list.

Since the beginning of Spring 2020, more workouts have been included. Please get in touch with the author if you have any criticism or recommendations, or if you plan to utilize the book in a course that you are teaching.

Get the book

In the form of an interactive online ebook, the full book is available for free. This should work on all screen sizes, including smart phones, with minimal modification. Hints and solutions to examples and exercises are concealed, but may be easily accessed by clicking on the links to the examples and exercises. Some exercises also allow you to enter and check your work, allowing you to attempt the task numerous times without revealing the solution. A free pdf version, appropriate for reading on a tablet or computer, is available for download for those who want to read their documents offline.

Hints and solutions (where available) may be obtained by selecting the exercise number from the drop-down menu, and selecting the number of the hint or solution will return you to the exercise.

This should be less expensive than printing and binding the complete book from the ground up.

PreTeXt (and LaTeX) source

A free interactive online ebook of the complete book is available for download. Everything, even smart phones, should be compatible with this. A hint or solution to an example or an exercise is buried, but may be quickly exposed by selecting one of the links to such examples or exercises. A few exercises also allow you to input and check your work, allowing you to attempt the exercise numerous times without revealing the solution. In case you want to read it on your tablet or computer without having to connect to the internet, you may download a free pdf version for offline use.

Hints and solutions (where available) may be obtained by selecting the exercise number from the drop-down menu, and selecting the number of the hint or solution will return you to the original exercise.

If you print the complete book and bind it yourself, this should be less expensive than the alternative.

Instructor resources

When utilizing the book in a class that you are teaching, instructor resources are accessible upon request. If you are using the book in a class you are teaching, instructor materials are available upon request. Simply get in touch with the author. If you have access to a WeBWorK server, you may also request homework sets from the WeBWorK server (otherwise, consider using the reasonably pricedEdfinity).

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About the book

Beginning as a series of lecture notes for a discrete mathematics course at the University of Northern Colorado, the text evolved into what it is today. This course provides as an introduction to issues in discrete mathematics as well as a “introduction to proofs” course for math students who are not already familiar with proofs. In most cases, the course is taught with a significant degree of student inquiry, and this work is meant to assist with that. Counting, sequencing, logic, and graph theory are the four key subjects studied in this course.

Students will develop acquainted with the language of mathematics through an introduction chapter that covers mathematical statements, sets, and functions.

Two additional subjects (generating functions and number theory) are also covered. While the book originated as a collection of lecture notes, it has now developed a number of elements that should make it suitable for use as a main textbook, including:

  • There are 473 exercises total, with 275 having solutions and another 109 having suggestions. The exercises range from simple to complex, with many of the problems suited for homework. Explore!activities are sprinkled throughout the book to encourage active, inquiry-based learning
  • And A comprehensive index and symbol list
  • Page style and formatting that is consistent and useful (for example, examples that are simple to recognize, significant definitions and theorems in boxes, and so on)

About the author

Oscar Levin is a professor at the University of Northern Colorado and a member of the National Academy of Sciences. Over the course of his academic career, he has garnered several teaching accolades, including a number of national teaching prizes. In 2009, he graduated with honors from the University of Connecticut with a Ph.D. in mathematical logic.

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A lecturer at the University of Northern Colorado, Oscar Levin is an associate professor of mathematics. Over the course of his academic career, he has garnered several teaching accolades, including a National Merit Scholar Award. From the University of Connecticut, he got his Ph.D. in mathematical logic in 2009.

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