How can I access the index variable in map?

Anonymous Monk has asked for the wisdom of the Perl Monks concerning the following question: ⭐ (arrays)

# This works:

@a = (1,1,1);
@b = (2,2,2);
foreach $i (0 .. $#a) {
  $a[$i] += $b[$i];
}
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but I'd like to use map. Is there a way to access the map index [$i] variable so I can do something like this:

@a = map $a[$i] + $_, @b;
[download]

Or is it simply not worth it?

Originally posted as a Categorized Question.