Arithmetic Progression

Arithmetic Progression (A . P)

In a sequence the difference of any two consecutive terms is constant, then the sequence is called an arithmetic progression. That difference is called the common difference and is denoted by d.



Sequence တစ္ခုတြင္ ကပ္လွ်က္ရွိေသာ မည့္သည့္ကိန္းႏွစ္ခုမဆို ျခားနားျခင္း(ႏႈတ္ျခင္း) သည္ ကိန္းေသျဖစ္ လွ်င္ ၎ sequence ကို arithmetic progression ဟုေခၚသည္။



If u₁ , u₂ , u₃ , u₄ , - - -, u_n-1 , u_n is an A . P,then u₂ -u₁ = u₃ -u₂= u₄ -u₃ = - - - = u_n -u_n-1 = constant.

u_n -u_n-1 = d.

u_n = u_n-1 + d

Generally the first term (u₁₎ of a sequence is denoted by a.

Therefore ....

u₁ = a

u_n = u_n-1 + d

u₂ = u₁ + d = a + d

u₃ = u₂ + d = 2a + d

u₄ = u₃ + d = 3a + d

From above expression the n^th term of an arithmetic progression can be expressed as

un = a + (n-1)d

where ...

u_n = the n^th term

a = the first term

d = the common difference

n = number of term