How to make latest article use the excerpt on front page?

All you need to do is make use of the is_front_page() conditional tag.
You will also have to fetch the latest post using the WP_Query

Am example is shown below.

<?php 

$args = array(
'posts_per_page' => 1; //this fetch only the first recent post
);

$loop = new WP_Query( $args );
if ( $the_query->have_posts() ) :
while ( $the_query->have_posts() ) : $the_query->the_post();

if( is_front_page(): )
the_excerpt();
endif;

endwhile;
endif;

?>

Thanks Tublz, any idea exactly what I should edit in the Erudite theme?