# 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,
.

## 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 ?
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.
Moreover, a sequence a in a group G is an arithmetic progression of order h if and only if, for all n [greater than or equal to] 0,
that is, the sequence [([T.sup.*n][T.sup.n]).sub.n [greater than or equal to] 0] is an arithmetic progression of strict order m-1 in B(H).
In that situation both sequences [A.sub.1], [a.sub.2], [a.sub.3], [A.sub.4], [a.sub.5], [a.sub.6] and [b.sub.1], [b.sub.2], [b.sub.3], [b.sub.4], [b.sub.5], [b.sub.6] were arithmetic progressions. That meant that there existed constants c and k such that [a.sub.m+1] = [a.sub.m] + c and [b.sub.m+1] = [b.sub.m] + k for m = 1, 2, ...
(1.) If the sequences [a.sub.1], [a.sub.2], [a.sub.3], [a.sub.4], [a.sub.5], [a.sub.6] and [b.sub.1], [b.sub.2], [b.sub.3], [b.sub.4], [b.sub.5], [b.sub.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).
can be extended analytically to a meromorphic function with poles at arithmetic progression on a negative real semi-axis.
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 ...
Green and Tao are now trying to pin down the location of prime arithmetic progressions more precisely.

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