Thursday, May 16

Progression definition



Progression definition – it means progress, growth, gain, move forward or instantaneous changes in forward direction. Electromagnetic waves travel forward. It means they are progressing. Plant is growing, it means it is progressing.
Patient health is improving or progressing. The student is progressing; it means that the student is passing his examinations from lower class to higher class. It is the progress in positive or negative direction. Speed may be increased or decreased. It may have acceleration or retardation both.

In mathematics there are three types of progressions.
Arithmetic progression(A.P) :- this take place according to a certain formula, for example
a, a+d, a+2d, a+3d, …………………a+(n-1)d
where a=initial or first term,
d= common difference between the two terms.
n= number of terms

Example1: 1,3,5,7………………..nth term
Sequence of terms is arranged in such a manner so that the difference of any two successive terms of the sequence remains constant

Geometric progression (G.P) :-The rule or formula for G.P is as under.
a,ar,ar²,ar³,…………………..ar^(n-1)
where a=initial or first term,
r= common ratio between the two terms.
n= number of terms
 Sequence of terms is arranged in such a manner so that the ratio of any two successive terms of the sequence remains constant
Harmonic Progression:- a H.P. is the reciprocals of an arithmetic progression. The form of HP is
1/a1,1/a2……………………
a1, a2, a3… is called an HP if  1/a1,1/a2..is an HP.
If a, b, c are in HP, then b is the harmonic mean between a and c.
In this case, b = 2ac/(a+c)
Examples are
12, 6, 4, 3,  , 2, … ,
10, 30, -30, -10, -6, -  , … ,

Progression In other fields:
Astrological:- It is used in Horoscope astrology for  forecast of future happenings
Horizontal:- the gradual movement from left to right or right to left of  a line .
Age:- the process of modification of a photograph of a person show  the  aging effect.
Tax: is a tax in which the amount of tax id directly proportional to the amount of income tax rate is increased as the income amount is increased.
Semantic:- It is the evolution of used word
Color:- the whole ranges of color for which the values changes smoothly through hues, and saturation, along with the illumination, or the combination of all these three factors.
Educational:- It is the progress of the  individual from lower classes to higher class.
Age:- the process of modification of a photograph of a person show  the  aging effect.
Tracking purpose:-It is used in video games to check the performance of the individuals.

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