GEOMETRIC PROGRESSION Meaning and
Definition
-
A geometric progression, also known as a geometric sequence, is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. The common ratio, denoted as 'r', remains constant throughout the sequence, thereby defining the pattern of growth or decay.
Mathematically, a geometric progression can be expressed in the form an = a1 * r^(n-1), where 'an' represents the nth term of the sequence, 'a1' is the first term, 'n' denotes the position of the term in the sequence, and 'r' signifies the common ratio. The first term, a1, serves as the starting point or initial value, while subsequent terms are obtained by multiplying a1 by r.
The properties of a geometric progression depend on the value of the common ratio. If the common ratio is greater than 1, the sequence grows exponentially, with each term being larger than the previous. Conversely, if the common ratio is between 0 and 1, the sequence decays or shrinks, with each term being smaller than the previous. In both cases, the magnitude of the common ratio determines the rate of growth or decay.
Geometric progressions have various applications across fields such as finance, physics, engineering, and computer science, where exponential or decaying patterns are encountered. Understanding geometric progressions and their properties allows for the prediction of future terms, determination of total sums, time estimations, and analysis of growth or decay rates within a given sequence.
Common Misspellings for GEOMETRIC PROGRESSION
- feometric progression
- veometric progression
- beometric progression
- heometric progression
- yeometric progression
- teometric progression
- gwometric progression
- gsometric progression
- gdometric progression
- grometric progression
- g4ometric progression
- g3ometric progression
- geimetric progression
- gekmetric progression
- gelmetric progression
- gepmetric progression
- ge0metric progression
- ge9metric progression
- geonetric progression
Etymology of GEOMETRIC PROGRESSION
The word "geometric" is derived from the Greek word "geōmetrikos", which means "relating to geometry". It is a combination of "geō" (earth) and "metron" (measure).
The term "progression" comes from the Latin word "progressio", which means "a moving forward" or "advancement". It is derived from the verb "progredi", which combines "pro" (forward) and "gradi" (to walk or step).
Therefore, the etymology of the term "geometric progression" suggests that it refers to a measure or advancement in a forward or step-like manner, based on geometric principles.
