sub geometric {
    my @known = @_;

    my $prev = shift @known;
    my $curr = shift @known;
    return undef if ! $prev;
    my $factor = $curr / $prev;
    while ( @known ) {
        $prev = $curr;
        $curr = shift @known;
        return undef if ! $prev;
        return undef if $factor != $curr / $prev;
    }

    return $curr * $factor;
}

sub arith {
    my @known = @_;

    my $prev = shift @known;
    my $curr = shift @known;
    my $diff = $curr - $prev;
    while ( @known ) {
        $prev = $curr;
        $curr = shift @known;
        return undef if $diff != $curr - $prev;
    }

    return $curr + $diff;
}

sub series {
    my @known = @_;

    return undef if scalar @known < 2;

    my @next_gen = ( \&arith, \&geometric );
    my @next = grep { defined } map { $_->( @known ) } @next_gen;

    return undef if scalar @next != 1;
    return $next[0];
}