How are the 'starting input' and 'starting output' defined in the context of arithmetic sequences?

In arithmetic sequences, the starting input is the initial x-value, and the starting output is the corresponding f(x) value when x is the starting input.

What does the 'common difference' represent in an arithmetic sequence?

The common difference is the constant value added or subtracted between consecutive terms in an arithmetic sequence.

What is a defining characteristic of arithmetic sequences regarding their rate of change and function type?

Arithmetic sequences have a constant rate of change and are represented by a linear function.

Cool Math Stuff: Arithmetic Sequence Study Notes

Open

Vinita

6/18/2023

Algebra 1

Arithmetic Sequences

Subjects

Algebra 1

Sequences

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

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 (common difference)

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

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

When the starting input is 1: Output(x) = Starting output ± Common difference (x-1)
When the starting input is 0: Output(x) = Starting output ± Common difference (x)

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: f(x) = 2 + 2(x-1) For Example #2: f(x) = 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.

Test your knowledge 💡💯

How do you calculate the output of an arithmetic sequence when the starting input is 1?

When the starting input is 1, the output of an arithmetic sequence is calculated by dividing the starting output by the common difference.

When the starting input is 1, the output of an arithmetic sequence is calculated by adding the product of the common difference and (x-1) to the starting output.

When the starting input is 1, the output of an arithmetic sequence is calculated by subtracting the common difference from the starting output.

When the starting input is 1, the output of an arithmetic sequence is calculated by multiplying the common difference by the starting output.

Can't find what you're looking for? Explore other subjects.

Math 7th Grade

Arithmetic

Algebra

Math 6th Grade

Pre-algebra

AP Biology

Math 8th Grade

Biology

Algebra basics

Physics

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

17 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

Algebra 1

Sequences

Introduction to Arithmetic Sequences

Cool Math Stuff: Arithmetic Sequence Study Notes

Vinita

@galaxyvinita

17 Followers

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

9th/8th

Algebra 1

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 content. It'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 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 (common difference)

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

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

When the starting input is 1: Output(x) = Starting output ± Common difference (x-1)
When the starting input is 0: Output(x) = Starting output ± Common difference (x)

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: f(x) = 2 + 2(x-1) For Example #2: f(x) = 1 + 3x

Vocabulary: Term - A number in a sequence.

Sign up to see the content. It'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 (independent variable) and a starting output (dependent 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 (common difference)

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

x | f(x) 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.

Test your knowledge 💡💯

Which equation represents an arithmetic sequence with a starting input of 0, a starting output of 1, and a common difference of 3?

Given a starting input of 0, a starting output of 1, and a common difference of 3, the equation f(x) = 1 + 3x correctly represents the arithmetic sequence.

Given a starting input of 1, a starting output of 1, and a common difference of 3, the equation f(x) = 1 + 3(x-1) correctly represents the arithmetic sequence.

Given a starting input of 1, a starting output of 0, and a common difference of 3, the equation f(x) = 3 + x correctly represents the arithmetic sequence.

Given a starting input of 0, a starting output of 3, and a common difference of 1, the equation f(x) = 3 + x correctly represents the arithmetic sequence.