# How do you tell whether the sequence -1,1,3,5,.... is arithmetic, geometric or neither?

##### 1 Answer

Jun 8, 2018

The sequence is arithmetic

#### Explanation:

A sequence

- Arithmetic if the
**difference**between two consecute elements, i.e.#a_n-a_{n-1}# , is constant. - Geometric if the
**ratio**between two consecute elements, i.e.#a_n/a_{n-1}# , is constant.

Let's test both to get the answer.

**Difference test**

Let's consider the difference between every element and the following one:

#a_2-a_1= 1-(-1)=1+1=2# #a_3-a_2 = 3-1=2# #a_4-a_3 = 5-3=2#

The difference remains constant (it's always

**Ratio test**

Let's consider the ratio between every element and the following one:

#a_2/a_1= 1/(-1)=-1# #a_3/a_2 = 3/1=3# #a_4/a_3 = 5/3=1.666...#

The ratio is always different, so the sequence is not geometric, as expected.