Arithmetic progression

To verify that the given sequence is an 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 common difference of 2.

If the first term of an arithmetic progression is a_{1} and the common difference of successive members is d, then the nth term of the sequence (a_{n}) is given by:

a_{n} = a_{1} + (n - 1)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.

1- Sequence of 1,4,7,10.......( This is an AP)

2- Sequence of 1,4,6,9........( This is not an AP)