Question

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

Answer 1

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:
`color(white)("XXX")a_i=a_(i-1)+10`
which would be an arithmetic sequence.

Since
`-8*c=2 rarr c=color(blue)(-4)`
and
`2*(color(blue)(-4)) != 10`
We can assert that this is not a geometric sequence.
(A geometric sequence requires:
`color(white)("XXX")a_i = a_(i-1)*c` for some constant `c`)