Answer
$r=-\frac{1}{2}$
Work Step by Step
The common ratio for the geometric sequence:
$\frac{1}{3},-\frac{1}{6}, \frac{1}{12}, -\frac{1}{24}$
is
$r=\frac{a_{n+1}}{a_n}$
$r=\frac{a_2}{a_1}=\frac{-\frac{1}{6}}{\frac{1}{3}}=-\frac{1}{2}$
Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
by Bittinger, Marvin L.; Ellenbogen, David J.; Johnson, Barbara L.
Published by
Pearson
ISBN 10:
0-32184-874-8
ISBN 13:
978-0-32184-874-1
Chapter 14 - Sequences, Series, and the Binomial Theorem - Connecting: The Concepts - Exercises - Page 909: 2
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