ARITHMETICAL PROGRESSION Meaning and
Definition
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Arithmetical progression, also known as an arithmetic sequence, is a fundamental concept in mathematics that refers to a sequence of numbers in which the difference between any two consecutive terms is constant. This common difference is denoted by the letter "d" and is usually a whole number.
In an arithmetical progression, each term can be obtained by adding the common difference to the preceding term. For example, if the first term of the sequence is "a" and the common difference is "d", the second term will be "a + d", the third term will be "a + 2d", and so on.
The main characteristic of an arithmetical progression is its sequential and predictable nature. As each term follows the same established pattern, it becomes simpler to determine the value of any term in the sequence. This allows for easy calculations and identification of specific terms within the progression.
Arithmetical progressions play a crucial role in numerous applications, including mathematics, physics, and finance. They are used to model various real-world scenarios, such as the growth of populations, increase in investment returns, or progression of time. Moreover, they lay the foundation for more complex mathematical concepts and are essential in understanding mathematical series, summations, and inequalities.
Overall, an arithmetical progression provides a systematic and clear representation of a sequence of numbers, highlighting the relationship between terms and aiding in the analysis and prediction of numerical patterns.
Common Misspellings for ARITHMETICAL PROGRESSION
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Etymology of ARITHMETICAL PROGRESSION
The word "arithmetical" originates from the Middle French word "arithmetique", which derived from the Latin word "arithmetica". In turn, the Latin term came from the Greek word "arithmētikē", which means "the art of numbers".
The term "progression" originated from the Latin word "progressio", which derived from the verb "progredi", meaning "to proceed or go forward". Thus, "arithmetical progression" signifies a sequence of numbers that continuously moves forward or proceeds through subsequent terms based on a fixed arithmetic pattern.
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