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Sequence

Source: 1997 National High School Mathematics League, Exam One, Problem 1

March 4, 2020

Problem Statement

Squence (xn)(x_n) satisfies that xn+1=xn−xn−1(n≥2)x_{n+1}=x_n-x_{n-1}(n\geq2). If x1=a,x2=bx_1=a,x_2=b, Sn=x1+x2+⋯+xnS_n=x_1+x_2+\cdots+x_n. Wich one is correct? (A)x100=−a,S100=2b−a\text{(A)}x_{100}=-a,S_{100}=2b-a (B)x100=−b,S100=2b−a\text{(B)}x_{100}=-b,S_{100}=2b-a (C)x100=−a,S100=b−a\text{(C)}x_{100}=-a,S_{100}=b-a (D)x100=−b,S100=b−a\text{(D)}x_{100}=-b,S_{100}=b-a
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