Question

Is -13, -6, 1, 8 arithmetic?

Answer 1

Given the following sequence

`\lbrace-13,-6,1,8,\ldots\rbrace`

We want to know if this sequence is arithmetic. The general term of an arithmetic sequence is given by

`a_n=a_1+(n-1)d`

Where d represents the common ratio. An arithmetic sequence increases by the same value every term(this value is the common ratio). If the difference between neighbor terms is the same for all of our terms, this sequence can be written as an arithmetic sequence.

Let's calculate the difference between the terms

`\begin{gathered} a_2-a_1=-6-(-13)=-6+13=7 \\ a_3-a_2=1-(-6)=1+6=7 \\ a_4-a_3=8-1=7 \end{gathered}`

Since the difference is the same, this sequence is Arithmetic.