Question

Find the two missing terms of the sequence and determine if the sequence is arithmetic, geometric, or neither.

3, 1, -1, -3, __, __ ​

Answer 1

`-5,-7`

It is Arithmetic.

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" (
`r`).

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
`d`.

Then, given the following sequence:

`3, 1, -1, -3`

- Let's find out if it is geometric by dividing each term by its previous one. Then:

`(-3)/(-1)=3\\\\(-1)/(1)=-1`

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:

`-3-(-1)=-2\\\\-1-1=-2\\\\1-3=-2`

You can idenfity that it has a Common difference:

`d=-2`

Therefore, it is an Arithmetic sequence.

The next to terms are:

`-3-2=-5\\\\-5-2=-7`