Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 835: 56

$x=1$

In order to make the terms $2x$, $3x+2$, and $5x+3$ as consecutive terms in an arithmetic sequence, we must have a common difference between the terms. For this, we have: $(5x+3)-(3x+2) =(3x+2) -(2x)$ This yields: $2x+1=x+2$ or, $2x-x=2-1$ or, $x=1$