Answer:
[tex]-5,-7[/tex]
It is Arithmetic.
Step-by-step explanation:
1) A sequence is geometric when it goes from a term to the next term by multiplying by the same number, which is called "Common ratio" ([tex]r[/tex]).
2) A sequence is arithmetic when it goes from a term to the next term by adding or subtracting a common value. This value is called "Common difference" and it is denoted with [tex]d[/tex].
Then, given the following sequence:
[tex]3, 1, -1, -3[/tex]
- Let's find out if it is geometric by dividing each term by its previous one. Then:
[tex]\frac{-3}{-1}=3\\\\\frac{-1}{1}=-1[/tex]
Since there is no Common ratio, it is not a Geometic sequence.
- Now let's see if it is arithmetic by subtracting each term by its previous one:
[tex]-3-(-1)=-2\\\\-1-1=-2\\\\1-3=-2[/tex]
You can idenfity that it has a Common difference:
[tex]d=-2[/tex]
Therefore, it is an Arithmetic sequence.
The next to terms are:
[tex]-3-2=-5\\\\-5-2=-7[/tex]
