Addition of six numbers: a-3+a-2+a-1+a+1+a+2 =102, A = 35/2, which is self-contradictory.
Nine numbers add up: A-4+A-3+...+A+...+A+3+A+4 =102, 9 * A = 102, A = 35/3, which is contradictory.
The number 12 has been added: a-6+a-5+...+a+4+a+5 =102, 12A = 108, and a = 9, that is, 3.
Addition of more numbers: the minimum addition of 15 natural numbers is 0+1+2+...+14 =105 >102.