# How do you tell whether the sequence -8, 2, 12.... is arithmetic, geometric, or neither?

Oct 17, 2015

The given sequence could be arithmetic.

#### Explanation:

With so few terms, it is impossible to say for certain
however there appears to be a relationship between the terms of the form:
$\textcolor{w h i t e}{\text{XXX}} {a}_{i} = {a}_{i - 1} + 10$
which would be an arithmetic sequence.

Since
$- 8 \cdot c = 2 \rightarrow c = \textcolor{b l u e}{- 4}$
and
$2 \cdot \left(\textcolor{b l u e}{- 4}\right) \ne 10$
We can assert that this is not a geometric sequence.
(A geometric sequence requires:
$\textcolor{w h i t e}{\text{XXX}} {a}_{i} = {a}_{i - 1} \cdot c$ for some constant $c$)