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

1 Answer
Oct 17, 2015

Answer:

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#)