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mathematic progression

mathematic progression

04/24/2021
Arithmetic Progression
Edubomb Edubomb

ARITHMETIC PROGRESSION (AP) In mathematics

Any sequence whose terms are increase or decrease by the constant numbers is called the arithmetic progression. It means each term in the progression are differ by constant term except the first term. This constant number by which terms are differ called the common difference. 


Remember:

a.   Any sequence t1, t2, t3 …. will be in AP if t2

- t1 = t3- t2 = t­n-t(n-1)

b.   Any three-number a, b, c will be in sequence if b-a=c-b

c.    If constant is added, subtracted, multiplied, or divided to each term of an AP then the remaining term will be in progression.

d.   Any three numbers in AP can be written as a-d, a, a+d and any four numbers in AP can be written as a-3d, a-d, a+d, a+3d. and any five numbers in AP can be written as the a-2d, a-d, a, a+d, a+2d.

SOLVED EXAMPLES

Example-1; Show that the progression 21, 16, 11, 6, 1, … is an AP. Write its first term and the common difference. Which term of this AP is –54?

Solution:

Example-2; find the nth term and 19th term of the sequence 5, 2, -1, -4.

 

Solution:

We have given progression is 5, 2, -1, -4. since all term has common difference hence, we can conclude that given progression is in AP.

Hence first term a=5 and common difference d=-3


Example-3 Is 319 a term of the AP 11, 17, 23, 29, 35, …?

Solution:

 In the given AP, we have first term a = 11, common difference d = 6 now, let's assume that the nth term is 319 then we have a general term







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