This can easily be done using eval(), even under strict:

use strict;
my $a1 = 3;
my $a2 = 4;
my $a3 = 5;

my $sum = 0;

for ( 1..3 )
{
    eval "\$sum += \$a$_";
}

print $sum;
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p.s.
i personally would prefer to rewrite the script you have to update (as stated in previous post), because not doing so is false lazyness in my eyes.