# progression

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Related to progression: geometric progression

## progression,

in mathematics, sequencesequence,
in mathematics, ordered set of mathematical quantities called terms. A sequence is said to be known if a formula can be given for any particular term using the preceding terms or using its position in the 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, called the common difference. It has the general form a, a+d, a+2d, … , a+(n−1)d, … , where a is some number and a+(n−1)d is the nth, or general, term; e.g., the progression 3, 7, 11, 15, … is arithmetic with a=3 and d=4. The value of the 20th term, i.e., when n=20, is found by using the general term: for a=3, d=4, and n=20, its value is 3+(20−1)4=79. An arithmetic seriesseries,
in mathematics, indicated sum of a sequence of terms. A series may be finite or infinite. A finite series contains a definite number of terms whose sum can be found by various methods. An infinite series is a sum of infinitely many terms, e.g.
is the indicated sum of an arithmetic progression, and its sum of the first n terms is given by the formula [2a+(n−1)d]n/2; in the above example the arithmetic series is 3+7+11+15+… , and the sum of the first 5 terms, i.e., when n=5, is [2·3+(5−1)4] 5/2=55. A geometric progression is one in which each term is derived by multiplying the preceding term by a given number r, called the common ratio; it has the general form a, ar, ar2, … , arn−1, … , where a and n have the same meanings as above; e.g., the progression 1, 2, 4, 8, … is geometric with a=1 and r=2. The value of the 10th term, i.e., when n=10, is given as 1·210−1=29=512. The sum of the geometric progression is given by the formula a(1−rn)/(1−r) for the first n terms. A harmonic progression is one in which the terms are the reciprocals of the terms of an arithmetic progression; it therefore has the general form 1-a, 1-(a + d), … , 1-[a+(n−1)d]. This type of progression has no general formula to express its sum.

## Progression

A gradual increase in the size or shape of a form or design, keeping the same basic theme or idea.

## progression

[prə′gresh·ən]
(mathematics)
A sequence or series of mathematical objects or quantities, each entry determined from its predecessors by some algorithm.
(metallurgy)
The fixed dimension between adjacent stations in a progressive die and thus the precise distance the strip must advance between successive cycles of the press.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## progression

1. Maths a sequence of numbers in which each term differs from the succeeding term by a constant relation
2. Music movement, esp of a logical kind, from one note to the next (melodic progression) or from one chord to the next (harmonic progression)
3. Astrology one of several calculations, based on the movement of the planets, from which it is supposed that one can find the expected developments in a person's birth chart and the probable trends of circumstances for a year in his life
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
"We have an eclectic mix of styles on offer across the music spectrum and aim for our academy to be a progression route towards helping develop professional careers in the music industry."
KEYTRUDA, as a single agent, is indicated for the treatment of patients with recurrent or metastatic HNSCC with disease progression on or after platinum-containing chemotherapy.
In a secondary analysis of data from the ELITE trial, Sriprasert and colleagues dug deeper to assess the impact of plasma E2 levels on progression of subclinical atherosclerosis.
Employee progression has become relevant in the facility management industry, as clients seek to move to a new generation of contracts.
However, the letter noted that extension of schedule would have little impact on career progression of PMS/PCS officers due to the apportionment formula of 1993 wherein major share went to the officers of Pakistan Administrative Service.
Most studies have emphasized mean time to progression, which is generally said to be about 8 years.
'Since the establishment of my ministry in October 2016, there are 959 C band officers in post out of which 209 are already at C1 salary scale while 364 will be eligible for progression to different C band salary scales during financial year 2018/19,' he said.
Progression is flagged when the observed changes exceeds the predefined test-retest limits [5].
NAFL has generally been considered a benign condition, and it has been thought that only patients with NASH have a potential for fibrosis progression and cirrhosis development.
Objective: To evaluate the effects of blood lipid stability on progression of carotid atherosclerosis.
Although ET is typically able to delay disease progression, almost invariably, patients will experience relapse of their disease.
Other studies using the European Organization for Research and Treatment of Cancer 30-item core QoL questionnaire (EORTC QLQ-C30) indicate that disease progression is associated with a 30.26-point decline in Global Health Status [11].

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