Important thing here is to recognize the pattern,
a1 = 3
a2 = -1
a3 = 6
a4 = -2
an = an-4 which means,
a5 = a1
a6 = a2
a7 = a3
a8 = a4 and again
a9 = a5 = a1
a10 = a6 = a2 and so on...
so the values repeat after interval of 4;
3,-1,6,-2,3,-1,6,-2,..... etc
addition of first 4 terms = 3 + -1 + 6 + -2 = 6
addition of next 4 terms = addition of first 4 terms = 6
let's call this as addition of "1 group", so in first 80 terms we have 20 such groups
so addition of first 80 terms = 6 * 20 = 120
81st term = 3; 82nd term = -1 and 83rd term = 6
so addition of first 83 terms = 120 + 3 + -1 + 6 = 128
hence the answer C.
Hope this helps.
