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Cool Math Stuff: Arithmetic Sequence Study Notes

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Vinita

6/18/2023

Algebra 1

Arithmetic Sequences

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Sequences

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Introduction to Arithmetic Sequences

Cool Math Stuff: Arithmetic Sequence Study Notes

Arithmetic sequences and linear functions are explored in depth, focusing on their patterns, components, and graphical representations. This guide provides essential arithmetic sequence study notes to help students understand the relationship between sequences and linear functions.

  • Arithmetic sequences are defined by their constant difference between terms
  • The guide explains how to identify the starting input, starting output, and common difference in arithmetic sequences
  • Linear functions are connected to arithmetic sequences through their constant rate of change
  • Graphical representations and equations for arithmetic sequences are provided
  • Examples illustrate how to analyze and represent arithmetic sequences mathematically
...

6/18/2023

156

Arithmetic Sequence ALL types of sequences have a starting input & a starting out put 3 is the input foc) or y is the output independent var

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Page 2: Further Examples and Equations

This page continues with another example of an arithmetic sequence and introduces equations for finding terms.

Example #2 is presented:

Example: Starting input: 0, Starting output: 1, Pattern: Adds 3 each time commondifferencecommon difference

A table similar to the first example is provided, showing the relationship between x and fxx values.

The page then introduces equations for finding terms in arithmetic sequences:

  1. When the starting input is 1: Outputxx = Starting output ± Common difference x−1x-1
  2. When the starting input is 0: Outputxx = Starting output ± Common difference xx

Highlight: The choice of equation depends on whether the starting input is 0 or 1.

Examples of applying these equations are given:

For Example #1: fxx = 2 + 2x−1x-1 For Example #2: fxx = 1 + 3x

Vocabulary: Term - A number in a sequence.

This page reinforces the concept that arithmetic sequences can be represented as linear functions, with the slope representing the common difference and the y-intercept representing the starting output.

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Subjects

Algebra 1

Sequences

Introduction to Arithmetic Sequences

 

Algebra 1

•

156

•

Jun 18, 2023

•

2 pages

Cool Math Stuff: Arithmetic Sequence Study Notes

user profile picture

Vinita

@galaxyvinita

Arithmetic sequences and linear functions are explored in depth, focusing on their patterns, components, and graphical representations. This guide provides essential arithmetic sequence study notes to help students understand the relationship between sequences and linear functions.

  • Arithmetic sequences are defined... Show more

Arithmetic Sequence ALL types of sequences have a starting input & a starting out put 3 is the input foc) or y is the output independent var

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Page 2: Further Examples and Equations

This page continues with another example of an arithmetic sequence and introduces equations for finding terms.

Example #2 is presented:

Example: Starting input: 0, Starting output: 1, Pattern: Adds 3 each time commondifferencecommon difference

A table similar to the first example is provided, showing the relationship between x and fxx values.

The page then introduces equations for finding terms in arithmetic sequences:

  1. When the starting input is 1: Outputxx = Starting output ± Common difference x−1x-1
  2. When the starting input is 0: Outputxx = Starting output ± Common difference xx

Highlight: The choice of equation depends on whether the starting input is 0 or 1.

Examples of applying these equations are given:

For Example #1: fxx = 2 + 2x−1x-1 For Example #2: fxx = 1 + 3x

Vocabulary: Term - A number in a sequence.

This page reinforces the concept that arithmetic sequences can be represented as linear functions, with the slope representing the common difference and the y-intercept representing the starting output.

Arithmetic Sequence ALL types of sequences have a starting input & a starting out put 3 is the input foc) or y is the output independent var

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Introduction to Arithmetic Sequences

This page introduces the concept of arithmetic sequences and provides a detailed example.

An arithmetic sequence is defined as a sequence where the difference between consecutive terms is constant. The page explains that all sequences have a starting input independentvariableindependent variable and a starting output dependentvariabledependent variable.

Definition: An arithmetic sequence is a sequence where each term differs from the previous term by a constant amount, called the common difference.

The page presents Example #1 of an arithmetic sequence:

Example: Starting input: 1, Starting output: 2, Pattern: Adds 2 each time commondifferencecommon difference

A table is provided showing the relationship between input xx and output f(xf(x) values:

x | fxx 1 | 2 2 | 4 3 | 6 4 | 8

Highlight: Arithmetic sequences are linear functions because they have a constant rate of change.

The page also includes a visual representation of the sequence, showing how each point rises by 2 and moves right by 1 on a coordinate plane.

Vocabulary: Common difference - The constant value added to each term to get the next term in an arithmetic sequence.

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user