Answer:
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 {\displaystyle a_{1}}a_{1} and the common difference of successive members is d, then the nth term of the sequence ({\displaystyle a_{n}}a_{n}) is given by:
{\displaystyle \ a_{n}=a_{1}+(n-1)d}{\displaystyle \ a_{n}=a_{1}+(n-1)d},
and in general
{\displaystyle \ 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.
