Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises - Page 645: 5

$d=x+2y$

$\bf{\text{Solution Outline:}}$ To find the common difference of the given arithmetic sequence, $ x+3y,2x+5y,3x+7y ,$ 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= 2x+5y $ and $a_1= x+3y $, the common difference, $d$, is \begin{array}{l}\require{cancel}d=a_2-a_1\\\\ d=2x+5y-(x+3y) \\\\ d=2x+5y-x-3y \\\\ d=(2x-x)+(5y-3y) \\\\ d=x+2y .\end{array}