In known arithmetic sequence an, the sum of the first 30 items is 50, and the sum of the first 50 items is 30, then the sum of the first 80 items is

S50-S30=a31+a32
+… +a50= [20*(a31+a50)]/2=10(a31+a50)=10(a31+a80)=30-50=-20.
∴a1+a80=-2
∴S80=[80*(a1+a80)/2]=-80
Answer - 80
I've answered that before

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