mathematic progression
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 t_{1}, t_{2}, t_{3} …. will be in AP if t_{2}

t_{1} = t_{3} t_{2 }= t_{n}t_{(n1)}
b.
Any
threenumber a, b, c will be in sequence if ba=cb
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 ad, a, a+d and any four numbers in AP can be written as a3d, ad, a+d, a+3d. and any five numbers in AP can be written as the a2d, ad, a, a+d, a+2d.
SOLVED EXAMPLES
Example1; 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:
Example2; find the nth term and 19^{th}
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
Example3 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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