If an = an-4 for all n greater than 4, then a5 = a1, a6 = a2, a7 = a3, a8 = a4, a9 = a5 = a1, etc.
So the sequence is just:
2, -3, 5, -1, │ 2, -3, 5, -1, │ 2, -3, 5, -1 .... infinitely repeating
This repeats in blocks of four. The sum of the first four terms is 3. If we add the first 96 terms, we'll just be adding that same block of four terms 24 times; the sum will be
24 * 3 = 72.
If we add on the 97th term, which will be 2, we get the final answer: 72 + 2 = 74.