ARITHMETIC SERIES Meaning and
Definition
-
An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is constant. It is a mathematical progression that follows a specific pattern, where each term can be found by adding a constant value to the preceding term.
In an arithmetic series, the first term is denoted by 'a', and the common difference between the terms is represented by 'd'. Thus, the second term is 'a + d', the third term is 'a + 2d', and so on. The general formula to find the nth term of an arithmetic series is given by 'a + (n-1)d', where 'n' represents the position of the term.
The sum of an arithmetic series, also known as the arithmetic progression sum, can be calculated using different formulas. One common formula is the sum formula, which states that the sum of 'n' terms in an arithmetic series is equal to '(n/2)(2a + (n-1)d)'. Alternatively, the sum can be calculated by multiplying the average of the first and last terms by the number of terms.
Arithmetic series often find applications in various fields, including finance, physics, and computer science. They provide a foundation for calculating averages, predicting patterns, and solving problems that involve constant rate changes. Understanding arithmetic series helps in algebraic manipulations, pattern recognition, and making predictions based on past trends.
Common Misspellings for ARITHMETIC SERIES
- zrithmetic series
- srithmetic series
- writhmetic series
- qrithmetic series
- aeithmetic series
- adithmetic series
- afithmetic series
- atithmetic series
- a5ithmetic series
- a4ithmetic series
- aruthmetic series
- arjthmetic series
- arkthmetic series
- arothmetic series
- ar9thmetic series
- ar8thmetic series
- arirhmetic series
- arifhmetic series
- arighmetic series
- ariyhmetic series
Etymology of ARITHMETIC SERIES
The word arithmetic originated from the Greek word arithmos, which means number. It was later adapted into Latin as arithmeticus and eventually incorporated into Middle English as arithmetik. The term series has Latin roots and derives from the Latin word serere, meaning to join together or to link. Therefore, the combination of arithmetic and series in English led to the formation of arithmetic series.
Infographic
Add the infographic to your website:
