Display image for first sticky post only

Try this :

<ul>
<?php 

$args = array(
            'category_name' => 'महाराष्ट्र',
            'post__in' => get_option( 'sticky_posts' ),
            'showposts' => '6',

        );

$the_query = new WP_Query( $args );

  $count = 1;

    while ($the_query -> have_posts()) : $the_query -> the_post(); ?>

  <li>      
  <?php if ( 1 == $count ): ?>
<div class="thumbnail_class"><a title="<?php the_title(); ?>" href="https://wordpress.stackexchange.com/questions/150086/<?php the_permalink() ?>" rel="bookmark"><?php     the_post_thumbnail(array(342,173), array ('class' => 'alignleft1')); ?></a></div>

  <?php endif ?>

    <div class="link_contect"><a title="<?php the_title(); ?>" href="https://wordpress.stackexchange.com/questions/150086/<?php the_permalink() ?>" rel="bookmark"><?php     the_title(); ?></a></div><li>
      <?php 
    $count++;
    endwhile;

?>
</ul>

Here count variable used for detecting first post. It is initialized to 1. In another iteration its value is increased. so if condition would be false and does not display post image.

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