If "same length", then straightforward and perhaps not perlish, and idea originated before Discipulus's answer :). I wonder how inefficient this is compared to slurping/reading in large blocks, i.e. if read and seek 'cooperate' on input buffer (I don't know enough on underlying C calls).

use strict;
use warnings;
use autodie;

my $POS = 10;

open my $fh, '<', 'dna.txt';
my $L = length( <$fh> ) - 1;
seek $fh, $POS - 1, 0;

my ( $s, $i ) = ( '', 0 );
seek $fh, $L, 1
    while read $fh, $s, 1, $i++;

print "$s\n";
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