Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises - Page 645: 3

$d=-5$

$\bf{\text{Solution Outline:}}$ To find the common difference of the given arithmetic sequence, $ 3,-2,-7,-12,... ,$ subtract a term by its previous term. $\bf{\text{Solution Details:}}$ Since the common difference of an arithmetic sequence is the difference between a term and its previous term, then with $a_2= -2 $ and $a_1= 3 $, the common difference, $d$, is \begin{array}{l}\require{cancel} d=-2-3 \\\\ d=-5 .\end{array}