Notice how there are 39 numbers in the sequence, 78/2. Also notice how 2+78 = 80. We want to make this the easiest for us, so we should try to find all the pairs that sum to 80.
Seeing as there are 39 numbers, there will be one solo. that means there will be 19 pairs all summing to 80. 19*80 = 1520. But we are still missing one number. Since there are 19 pairs, our last integer will be in the center. Between the 19th integer and the 19th to last integer, 38 and 42, respectively, is 40. So adding them, our answer is 1,520 + 40 = 1,560.