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词汇 arithmetic-progression
释义 arithmetic progression
noun[ C or U ]
 mathematics specializeduk /ær.ɪθˌmet.ɪ.k prəˈɡreʃ.ən/ us /er.ɪθˌmet̬.ɪ.k prəˈɡreʃ.ən/(also arithmetic sequence, uk /ær.ɪθˌmet.ɪ.k ˈsiː.kwəns/ us /er.ɪθˌmet̬.ɪ.k ˈsiː.kwəns/); (also old-fashionedarithmetical progression, uk /ær.ɪθˌmet.ɪ.kəl prəˈɡreʃ.ən/ us /er.ɪθˌmet̬.ɪ.kəl prəˈɡreʃ.ən/)
a sequence (= an ordered series of numbers) in which the numbers get bigger or smaller by the same amount, such as 3, 6, 9..., or 9, 6, 3: 算术级数,等差数列,其中任何相邻两项以相同数量递增或递减,如3,6,9…, 或9,6,3
A computer search revealed an arithmetic progression consisting of 23 primes, the longest such sequence yet found.电脑搜索显示了一个由 23 个素数组成的等差数列,这是迄今为止发现的最长的此类数列。
Thus the terms 1, 4, 7, 10 form an arithmetic sequence.因此,1,4,7,10这四项构成一个等差数列。
Compare
geometric progression
In the following arithmetic progressions, the first three terms and the last term are given. Find the number of terms.
A squirrel is collecting nuts. It collects 5 nuts on the first day of the month, 8 nuts on the second, 11 on the third and so on in arithmetic progression.
Find which term of the arithmetic progression will next be equal to a term of the geometric progression.
All his sculptures are based on a sequence of numbers, an arithmetical progression.
They diminished the price of their produce in arithmetical progression.
SMART Vocabulary: related words and phrases

Numerical relationships
absolute difference
absolute error
absolute maximum
absolute minimum
boundary condition
differential
geometric progression
golden mean
golden ratio
harmonic progression
intersect
iteration
proportion
proportional
proportionally
proportionately
prorate
prorated
quantile
subset

Examples of arithmetic progression


arithmetic progression
It is easy to see that in each case the arithmeticprogression that we considered is a rainbow arithmeticprogression.
However, this contradicts our choice of the arithmeticprogression.
On sets of integers containing no k elements in arithmeticprogression.
Their successive capacities form an arithmeticprogression.
Due to mathematical properties of natural logarithm, the cycle lengths (periods) of oscillations, as an inverse of frequency, also form an arithmeticprogression after natural logarithmic transformation.
In fact, a monochromatic solution of the system above is a monochromatic arithmeticprogression of length k with the additional property that the difference has the same colour, too.
Specifically, the center frequencies and frequency ranges of oscillation bands with successively faster frequencies, from ultra-slow to ultra-fast frequency oscillations, form an arithmeticprogression on the natural logarithmic scale.
The constant intervals between oscillation bands on the logarithmic scale (arithmeticprogression) correspond to a constant ratio between the bands on the linear scale (geometric progression).
It is much fairer to have an arithmeticprogression of taxation relief rather than a geometric progression.
From the
Hansard archive

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0
He referred to a worrying arithmeticprogression of the basic pension from £5 this year to £3 next year and came up with £1.50 the following year.
From the
Hansard archive

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0
In the nature of an arithmeticprogression, it was four, two, four, six, four, six.
From the
Hansard archive

Example from the Hansard archive. Contains Parliamentary information licensed under the Open Parliament Licence v3.0
We owe him the general concept of factorial as a product of a finite number of terms in arithmeticprogression.
From
Wikipedia

This example is from Wikipedia and may be reused under a CC BY-SA license.
The behavior of the arithmeticprogression depends on the common difference "d".
From
Wikipedia

This example is from Wikipedia and may be reused under a CC BY-SA license.
A finite portion of an arithmeticprogression is called a finite arithmeticprogression and sometimes just called an arithmeticprogression.
From
Wikipedia

This example is from Wikipedia and may be reused under a CC BY-SA license.
The 30-60-90 triangle is the only right triangle whose angles are in an arithmeticprogression.
From
Wikipedia

This example is from Wikipedia and may be reused under a CC BY-SA license.
See all examples of arithmetic progression
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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