Arithmetic progression is a term used in mathematics to describe a sequence of numbers that are equally spaced apart. It is a fundamental concept in mathematics and is used in a wide variety of applications, from finance to physics.
Definitions
Arithmetic progression is defined as a sequence of numbers in which each term is obtained by adding a constant value to the previous term. The constant value is known as the common difference of the sequence.
Origin
The concept of arithmetic progression can be traced back to ancient Greek mathematicians such as Euclid and Pythagoras. It was further developed by Indian mathematicians such as Aryabhata and Brahmagupta, who used it in their works on algebra and arithmetic.
Meaning in different dictionaries
The meaning of arithmetic progression is consistent across different dictionaries. Merriam-Webster defines it as “a sequence of numbers in which each term is equal to the sum of the preceding term and a constant.” Oxford Dictionary defines it as “a sequence of numbers in which each term is obtained by adding a fixed number to the preceding term.”
Associations
Arithmetic progression is associated with a variety of mathematical concepts, including linear equations, geometric progressions, and series. It is also used in finance to calculate compound interest and in physics to describe the motion of objects.
Synonyms
Synonyms of arithmetic progression include arithmetic sequence, linear sequence, and constant difference sequence.
Antonyms
Antonyms of arithmetic progression include geometric progression, exponential growth, and non-linear sequence.
The same root words
The same root words as arithmetic progression include arithmetic, progress, and progression.
Example Sentences
- The arithmetic progression of 2, 4, 6, 8, 10 has a common difference of 2.
- The formula for the nth term of an arithmetic progression is given by a + (n-1)d, where a is the first term and d is the common difference.
- The sum of the first 10 terms of the arithmetic progression 3, 7, 11, 15, . is 190.
- An arithmetic progression can be used to model the growth of a savings account with compound interest.