Arithmetic progression

An Arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
If the initial term of an arithmetic progression is




a

1




{\displaystyle a_{1}}
and the common difference of successive members is d, then the nth term of the sequence (




a

n




{\displaystyle a_{n}}
) is given by:






a

n


=

a

1


+
(
n
−
1
)
d


{\displaystyle \ a_{n}=a_{1}+(n-1)d}
,and in general






a

n


=

a

m


+
(
n
−
m
)
d


{\displaystyle \ a_{n}=a_{m}+(n-m)d}
.A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.

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