# arithmetic progression

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Related to arithmetic progression: geometric progression, harmonic progression
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### (mathematics) a progression in which a constant is added to each term in order to obtain the next term

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As the eigenvalues of [GAMMA]/[PI] are in arithmetic progression and [rho] [greater than or equal to] 3, neither type (I), (IA), (II), (IIA) nor (III) can occur.
--The value of the median increases along with the increase of the arithmetic progression for each age group
We say that the sequence a is an arithmetic progression of strict order h = 0, 1, 2 ..., if h = 0 or if it is of order h > 0 but is not of order h - 1; that is, the polynomial p of (6) has degree h.
The continued fraction in (10.3) converges since the partial denominators are positive and are members of an arithmetic progression. To be more precise let us put [P.sub.1] = P, [P.sub.n] = [p.sup.2] n = 2,3 ...
The difference, argued Dewitt, is that Ponzi's swindle was a geometric progression that "works only so long as there is an ever-increasing number of new investors coming into the scheme." Social Security, by contrast, is a simple arithmetic progression that "is sustainable forever, provided that the number of new people entering the system maintains a rough balance with the number of people collecting from the system."
As an adjective in such phrases as arithmetic progression or arithmetic relationship, means in a constant additive way (e.g., 3, 6, 9, 12,...) as distinguished from a constant *geometric way (e.g., 3, 9, 27, 81,...).
In 1798 he published a book, Essay on Population, in which he pointed out that population tended to increase in geometric progression (2, 4, 8, 16...) while the food supply tended to increase in arithmetic progression (2, 3, 4, 5...).
Using the sum of an arithmetic progression with common difference 1, it can be shown that the nth triangular number is given by
[a.sub.kt+1], [a.sub.kt+2], [a.sub.kt+3], ..., akt+t is a finite arithmetic progression with [d.sub.1] as the common difference,where t is a constant natural numbers,
In general, a sequence (finite or infinite) is called an arithmetic progression if the difference of any term from its preceding term is constant.
Progressive primes A computer search revealed an arithmetic progression consisting of 23 primes, the longest such sequence yet found (sciencenews.org/ 20040828/mathtrek.asp).
* Its consonants occur in clusters, each separated by the vowel E, to form the basic arithmetic progression 1,2,3: P, PP, RTR.
What has just been performed is the sum of an arithmetic progression. An arithmetic progression (AP) is a sequence of numbers having the same difference between every pair of successive numbers.
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