#### Answer

$x=\dfrac{-3}{2}$

#### Work Step by Step

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, $x=\dfrac{-3}{2}$