Series, Sequences and Progressions

  • Context: High School 
  • Thread starter Thread starter Cheman
  • Start date Start date
  • Tags Tags
    Sequences Series
Click For Summary

Discussion Overview

The discussion revolves around the terminology of "series," "sequences," and "progressions" in mathematics. Participants explore the definitions and relationships between these concepts, referencing both textbooks and dictionaries.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant's textbook defines a progression as synonymous with a series, while a dictionary suggests it refers to a sequence.
  • Another participant cites a dictionary definition of progression as a simple sequence of numbers with a constant relation between terms, mentioning types like arithmetic, harmonic, and geometric progressions.
  • A recommendation is made for The Penguin Dictionary of Maths, noted for its affordability and user-friendly style for learners.
  • A later reply questions the textbook's definition, emphasizing that mathematically, a "series" typically refers to a sum, suggesting that the textbook may be using "series" in a more general sense akin to "sequence."

Areas of Agreement / Disagreement

Participants express differing views on the definitions of progression, series, and sequences, indicating that no consensus has been reached regarding the terminology.

Contextual Notes

There is a lack of clarity regarding the definitions used in different contexts, as well as the level of the textbook referenced, which may influence the understanding of these terms.

Cheman
Messages
235
Reaction score
1
Series, Sequences and Progressions...

My textbook says that a progression is another name for a series, but the dictionary says it is another name for a sequence - which is it?

Thanks.
 
Physics news on Phys.org
My soft cover Penguin Dictionary calls a progression, "A simple sequence of numbers in which there is a constant relation between consecutive terms," such as arithmetic, harmonic, and geometric.
 
Yep it's a sequence. Also I recommend The Penguin Dictionary of Maths, as it's cheap (only about £5) and it's style (compared to say the McGraw-Hill dictionary of maths) makes it ideal for anyone learning maths.
 
Cheman said:
My textbook says that a progression is another name for a series, but the dictionary says it is another name for a sequence - which is it?

Thanks.

I'm surprised that your textbook says that. Mathematically speaking a "series" is a sum but your textbook (what level is it?) may be using "series" as another word for "sequence"- which is common in general English usage.
 

Similar threads

Undergrad Why the different terminology: Sequence versus Series?
  • · Replies 11 ·
Replies
11
Views
2K
High School Understanding about Sequences and Series
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Delta sequence "extrapolation"
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Have you ever used "symbolic logic" to help you learn calculus?
  • · Replies 5 ·
Replies
5
Views
3K
How can we teach students the difference between sequences and series?
  • · Replies 8 ·
Replies
8
Views
2K
High School Can You Solve This Exercise on Arithmetic-Geometric Series?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Understanding the nth-term test for Divergence
  • · Replies 17 ·
Replies
17
Views
6K
Undergrad What is the official name for a Field Series in mathematics/physics?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Limit of a Sequence (Updated with progress)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Infinite Series of Infinite Series
  • · Replies 7 ·
Replies
7
Views
3K