Show excerpt for only first post in query

Question

You can use $wp_query->current_post in your loop to check the current post. You don’t need two loops, one will do the trick If you need excerpt for first post only, you can do something like this. Just remember, the first post in the loop is 0, and not 1

if ( !$wp_query->current_post > 0 ) :
   the_excerpt();
else :
   <--- DO SOMETHING ELSE FOR OTHER POSTS
endif;

For all the WP_Post member variables, go and check the link provided from the codex