Question

is the given sequence arithmetic?Why or why not(NO EXPLANATION NO WORK :))

Answer 1

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:

$1,2,4,7,\ldots$

Let's check it they have a common difference applying the procedure shown below:

$\begin{gathered} 2-1=1 \\ 4-2=2 \\ 7-4=3 \end{gathered}$

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.