Subjects

Pre-Calculus

Vectors

Vectors Word Problems

Learn About Arithmetic Sequences and Cool Patterns

Name: Knowunity
Brand: Knowunity

View

Learn About Arithmetic Sequences and Cool Patterns

eddie

@eddies_q

5 Followers

A comprehensive guide to understanding arithmetic sequences and common differences along with geometric sequences and their properties.

Arithmetic sequences are characterized by constant differences between consecutive terms, utilizing explicit and recursive formulas for calculations
Geometric sequences feature constant ratios between successive terms, employing specific formulas for term calculation
Both sequence types incorporate means (arithmetic and geometric) to find intermediate terms between given values
Key concepts include common differences, ratios, and specialized formulas for sequence manipulation

10/18/2023

191

TITLE. Arithmetic Sequences
always diverge
The difference between successive terms is constant
2,
+2 +2 +2
Common difference: an- an-s = d
"

View

Geometric Sequences

This section covers geometric sequences, their properties, and methods for calculating terms and means within these sequences.

Definition: A geometric sequence is characterized by a constant ratio between consecutive terms, known as the common ratio 'r'.

Vocabulary: Common ratio (r) is the constant value by which each term is multiplied to obtain the next term.

Example: In the sequence 1, 3, 9, 27, the common ratio is 3.

Highlight: The explicit formula for geometric sequences is an = a₁(r)^(n-1), where a₁ is the first term and r is the common ratio.

Example: Finding 3 geometric means between 2 and 162:

Initial terms: 2 and 162
Calculated means create a sequence with constant ratio
Process involves finding intermediate terms that maintain the geometric progression

View

Arithmetic Sequences

This section explores the fundamental concepts of arithmetic sequences, where consecutive terms maintain a constant difference. The content details how to identify and work with these sequences effectively.

Definition: An arithmetic sequence is a sequence where the difference between successive terms remains constant, denoted as the common difference 'd'.

Vocabulary: Common difference (d) represents the constant value added to each term to get the next term in an arithmetic sequence.

Example: In a sequence where terms progress as: 2, 4, 6, 8..., the common difference is +2.

Highlight: The explicit formula for finding any term in an arithmetic sequence is an = a₁ + d(n-1), where a₁ is the first term and n is the term number.

Example: Finding arithmetic means between -30 and -45:

Starting with -30
Common difference calculated as -5
Sequence progresses: -30, -35, -40, -45

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

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

15 M

Students use Knowunity

#1

In Education App Charts in 12 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

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Subjects

Pre-Calculus

Vectors

Vectors Word Problems

Learn About Arithmetic Sequences and Cool Patterns

eddie

@eddies_q

5 Followers

A comprehensive guide to understanding arithmetic sequences and common differences along with geometric sequences and their properties.

Arithmetic sequences are characterized by constant differences between consecutive terms, utilizing explicit and recursive formulas for calculations
Geometric sequences feature constant ratios between successive terms, employing specific formulas for term calculation
Both sequence types incorporate means (arithmetic and geometric) to find intermediate terms between given values
Key concepts include common differences, ratios, and specialized formulas for sequence manipulation

10/18/2023

191

10th/11th

Pre-Calculus

Geometric Sequences

This section covers geometric sequences, their properties, and methods for calculating terms and means within these sequences.

Definition: A geometric sequence is characterized by a constant ratio between consecutive terms, known as the common ratio 'r'.

Vocabulary: Common ratio (r) is the constant value by which each term is multiplied to obtain the next term.

Example: In the sequence 1, 3, 9, 27, the common ratio is 3.

Highlight: The explicit formula for geometric sequences is an = a₁(r)^(n-1), where a₁ is the first term and r is the common ratio.

Example: Finding 3 geometric means between 2 and 162:

Initial terms: 2 and 162
Calculated means create a sequence with constant ratio
Process involves finding intermediate terms that maintain the geometric progression

Arithmetic Sequences

Definition: An arithmetic sequence is a sequence where the difference between successive terms remains constant, denoted as the common difference 'd'.

Vocabulary: Common difference (d) represents the constant value added to each term to get the next term in an arithmetic sequence.

Example: In a sequence where terms progress as: 2, 4, 6, 8..., the common difference is +2.

Highlight: The explicit formula for finding any term in an arithmetic sequence is an = a₁ + d(n-1), where a₁ is the first term and n is the term number.

Example: Finding arithmetic means between -30 and -45:

Starting with -30
Common difference calculated as -5
Sequence progresses: -30, -35, -40, -45

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

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

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 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