Question

To my knowledge, the answer should be there is no difference since I found the sum, however the answer is something else,

Answer 1

In the first series, the summation applies to the whole (2n+3) inside
the parentheses, so the 3 gets summed up 5 times.

But in the second one, the summation only applies to the 2n , so
the 3 is only added after the summation is finished.

The difference between five 3s the first time and one 3 the second time
is your 12 .

Answer 2

The difference between them is 12 because :
the sum of first series is : 2 * ( 1 + 2 + 3 + 4 + 5  ) + 15;
the sum of the second series is : 2 * ( 1 + 2 + 3 + 4 + 5 ) + 3.