## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

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