I, too, think the OP smells of homework, but since others have chimed in, here's my contribution of a regex (but it doesn't handle enclosing double-quotes, left as an exercise for the OPer – perhaps another post?):

>perl -wMstrict -le
"my $rx = qr{ \A (?! (?i) .* \bfirst\b ) This .* \. \z }xms;
 print '----- output -----';
 for my $str (@ARGV) {
   print $str, $str =~ $rx ? ' M' : ' No M', 'atch';
   }
"
"This is first sentence."  "This is second sentence."
"This is the First Lady."  "This is the firstborn."
----- output -----
This is first sentence. No Match
This is second sentence. Match
This is the First Lady. No Match
This is the firstborn. Match
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