geometric progression

Friendly

Geometric Progression

Definition:
A geometric progression (often abbreviated as GP) is a sequence of numbers where each number after the first is found by multiplying the previous one by a fixed, constant number called the "common ratio."

Usage Instructions:

• When to Use: You can use the term "geometric progression" when discussing mathematics, especially in contexts involving sequences, series, and growth patterns.
• How to Use: You can say, "The numbers 2, 6, 18 form a geometric progression with a common ratio of 3."

Advanced Usage:

In advanced mathematics, you might encounter concepts related to geometric progressions, such as: - Geometric Series: This is the sum of the terms of a geometric progression. - Exponential Growth: Geometric progressions are often used to describe situations where quantities grow at a constant percentage rate, such as in finance or population studies.

Word Variants:

• Geometric: Related to geometry or shapes.
• Progression: A series of events or numbers that follow a certain pattern.

Different Meanings:

• In a broader sense, "progression" can refer to any sequence of events or developments, not just in mathematics. For example, "the progression of a story" refers to how the story develops over time.

Synonyms:

• Sequence
• Series (in the context of mathematics)

Idioms and Phrasal Verbs:

There aren't specific idioms or phrasal verbs related to "geometric progression," but you might hear phrases like: - "Making progress" (though this is more general and does not refer specifically to geometric progression).

Summary:

A geometric progression is a mathematical sequence where each term is obtained by multiplying the previous term by a constant.

Academic

Noun

1. (mathematics) a progression in which each term is multiplied by a constant in order to obtain the next term
   • 1-4-16-64-256- is the start of a geometric progression