arithmetic progression

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Related to Arithmetic progressions: geometric progressions

arithmetic progression:

see progressionprogression,
in mathematics, sequence of quantities, called terms, in which the relationship between consecutive terms is the same. An arithmetic progression is a sequence in which each term is derived from the preceding one by adding a given number, d,
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arithmetic progression

[¦a·rith¦med·ik prə′gresh·ən]
(mathematics)
A sequence of numbers for which there is a constant d such that the difference between any two successive terms is equal to d. Also known as arithmetic sequence.

arithmetic progression

a sequence of numbers or quantities, each term of which differs from the succeeding term by a constant amount, such as 3,6,9,12
References in periodicals archive ?
If in a six by six array in which all rows are translations of the first row, and the numbers in both the first row and column form arithmetic progressions, then the sum of any six numbers of the array, no two of which are in the same row or column, is six times the arithmetic mean of the numbers in the upper left and lower right corners of the array.
6] are both arithmetic progressions, then the APT property ensures that the sequences in the first row and column of Figure 5 will also be arithmetic progressions (both are translations of sequences assumed to be arithmetic progressions).
For centuries, mathematicians have wondered how many arithmetic progressions such as these exist among the set of prime numbers and how long the progressions can get.
The mathematicians then deduced that the prime numbers are arranged within the spread of almost-primes with enough regularity to ensure that the overall sequence of primes does indeed contain arithmetic progressions of every length.