On a single post, you may enable pagination. You may want the featured image or whatever content to only display on the first page. Here’s the code:

<?php global $page; if( $page == 1 ):?>
<?php // put content here you only want to display on the first page ?> 
<?php endif;?>

On an archive page, you may have pagination. You may have content you want to display only on the first page. Here’s the code:

<?php 
$paged = (get_query_var('paged') ) ? get_query_var('paged') : 1;
if ( 1 == $paged ):?>
<?php // put content here you only want to display on the first page ?> 
<?php endif; ?>