Series, Sequences and Progressions

In summary, a progression can be considered both a series and a sequence, but mathematically it is more commonly used as a synonym for a sequence.
  • #1
Cheman
235
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.
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 

What is a series?

A series is a sequence of numbers or terms that are added together. The result of adding the terms is called the sum of the series.

What is a sequence?

A sequence is a list of numbers or terms that follow a specific pattern or rule.

What is the difference between arithmetic and geometric sequences?

In an arithmetic sequence, each term is obtained by adding a constant value to the previous term. In a geometric sequence, each term is obtained by multiplying a constant value to the previous term.

What is a progression?

A progression is a sequence or series that follows a specific pattern or rule.

How can series, sequences, and progressions be applied in real-life situations?

Series, sequences, and progressions can be used in many fields such as mathematics, science, finance, and computer science. For example, in finance, the concept of compound interest follows a geometric progression, and in computer science, the Fibonacci sequence is used in algorithms for search and optimization.

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