Creating Accordians in WordPress Theme

As per you described, What I have got is you want to add class active to last published post by the user.

By seeing your output and HTML, It seems that active class is missing.

So to achieve that, we will add one dummy condition that will print class="active". I would also suggest that modify your $arg and make in DESC order to get last published post first.

Your final code will be something like this :

    <div class="humour">
        <h1 class="section_heading"> HUMOUR ON INDIAN INVESTMENT </h1>
        <dl>
            <?php 
                $args = array(
                        'post_type' => 'humour',
                        'order'     => 'DESC' //Add order to get post in DESC order
                        );
                $humour_query = new WP_Query($args);
                $i=0; //Take variable and assign it 0
                if ($humour_query->have_posts()) : while($humour_query->have_posts()) : $humour_query->the_post(); 
            ?>
            <?php 
                if($i==0): //This condition will be true only once as I have added increament at the end
                    echo "<dt id='post-".the_ID()."' class="active">";
                else:   
            ?>
            <dt id="post-<?php the_ID(); ?>">
            endif;  
                <h1 class="link_heading"><?php the_title(); ?></h1>
                <div>
                    <img src="https://wordpress.stackexchange.com/questions/173215/<?php print IMAGES; ?>/arrowdown.png" class="arrow" id="down"/>
                    <img src="<?php print IMAGES; ?>/arrowup.png" class="arrow" id="up"/>
                </div>                                  
            </dt>                       
            <dd>
                <p>
                    <?php  
                        $excerpt = get_the_excerpt();
                        echo string_limit_words($excerpt,25); 
                    ?>
                </p>
            </dd>
            <?php 
            $i++; //Incremented that variable so class wont be added from second post
            endwhile; 
            endif; ?>
        </dl>
    </div>

NOTE: I have assumed that accordion is working with class active.