For this problem, you have to actually have the sum first before you can even determine what the last digits of the sum are. To do this, one of the many methods is the listing method, or so what I'd like to call it.
List the adding sequence from the first number to the last one which is:
15 16 17 .... 36 37
Then, under the sequence is the reverse of the sequence.
15 16 17 ... 36 37
37 36 35 ... 16 15
When you add the first list to the second list, you would always get the same sum which is:
15 16 17 ... 36 37
37 36 35 ... 16 15
---------------------------
52 52 52 ... 52 52
Then, we need to know how many number are there involved in each sequence, so there would be 23 since when you find the difference, you aren't actually including 15. The difference would only count how many numbers are there to reach 37 when you start at 15.
This would mean that there would be 23 52s where their product is 1196.
Since the product involves the two sequence earlier, and we only need one, we divide the product by 2.
The answer would be 598.
The last digit would be 8.