Echo custom taxonomy slug

Here’s the correct syntax for what you’re trying to do, if there’s just the single value for the ‘series’ custom taxonomy slug that you’re trying to retrieve. You were passing the whole array to your echoed string. I made a new variable $series which pulls the first/only value in the $terms_slugs array. And simplified a few other things you didn’t need in there. 🙂

    <?php 
    $terms = get_the_terms( $post->ID, 'series' );
    if ($terms) {
        $terms_slugs = array();
        foreach ( $terms as $term ) {
            $terms_slugs[] = $term->slug;
        }
        $series = $terms_slugs[0];      
        echo "/assets/products/{$series}/logos/{$series}-logo.png";
    } else {
        echo "nothing to see here";
    }
    ?>