In order to solve this exercise you need to remember the following: In an Arithmetic sequence, there next consecutive term is obtained by adding or subtracting a constant. This constant is called "Common difference".
In this case, you have the following sequence:
[tex]1,2,4,7,\ldots[/tex]Let's check it they have a common difference applying the procedure shown below:
[tex]\begin{gathered} 2-1=1 \\ 4-2=2 \\ 7-4=3 \end{gathered}[/tex]You can notice that there is not a Common difference between the consecutive terms. Therefore, it is not an Arithmetic sequence.
The answer is: It is not an Arithmetic sequence, because there is not Common difference between the consecutive terms.