arithmetic progression

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Explanation of "Arithmetic Progression"

Definition:
An "arithmetic progression" is a sequence of numbers in which each number (called a term) is obtained by adding a constant value to the previous term. This constant value is known as the "common difference."

Example:

A simple example of an arithmetic progression is:
1, 4, 7, 10, 13...
In this sequence, we start with 1 and add 3 each time (the common difference is 3).

Advanced Usage:

In more advanced mathematics, arithmetic progressions can be used to solve problems involving series and sums. For instance, the formula for the sum of the first n terms of an arithmetic progression is:
[ Sn = \frac{n}{2} (a + l) ]
where ( Sn ) is the sum, ( n ) is the number of terms, ( a ) is the first term, and ( l ) is the last term.

Word Variants:

• Arithmetic (adjective): Relating to arithmetic or numbers.
• Progression (noun): The process of developing or moving towards a more advanced state.

Different Meanings:

• In a broader context, "progression" can refer to any sequence or development of events or steps, not just in mathematics. For example, "the progression of a story" refers to how the plot develops.

Synonyms:

• Sequence
• Series
• Linear sequence

Idioms and Phrasal Verbs:

While "arithmetic progression" doesn’t have specific idioms or phrasal verbs associated with it, you might encounter phrases that use "progression" in a more general sense, such as: - "In the progression of time" – This refers to the way time moves forward. - "A step-by-step progression" – This means moving forward slowly and carefully, one step at a time.

Summary:

An arithmetic progression is a simple but important concept in mathematics involving a sequence of numbers where a constant is added to each term.

Academic

Noun

1. (mathematics) a progression in which a constant is added to each term in order to obtain the next term
   • 1-4-7-10-13- is the start of an arithmetic progression