Perhaps...

#!/usr/bin/perl -w
use strict;

my $somepath = "path to write to..";

my @arr_file=("R25_s_5_seq_18-26_alignment.txt",
              "R20_s_6_seq_18-26_alignment.txt");

open (FINAL, '>', $somepath) or 
        die "cannot open $somepath for write $!";
           
foreach my $file (@arr_file)
{
   open (FILE, '<', $file) or die "cannot open $file for reading $!";
   
   while ( my $line=<FILE> )
   {
      my ($important_thing) = (split(/\s+/,$line))[2];
      print FINAL "$important_thing\n";
   }
}
[download]

This is actually just a command line grep.
Type "man grep" at the command prompt.