已知数列(xn)满足Xn+1=Xn-Xn-1(n大于等于2),x1=a,x2=b,记Sn=x1+x2+…+xn,则下列结论正确的是(）A.X100=-a,S100=2b-aB.X100=-b,S100=2b-aC.X100=-b,S100=b-aD.X100=-a,S100=b-a请简要写出解答过程.谢谢!!!
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Xn+1=Xn-Xn-1=Xn-1-Xn-2-Xn-1=-Xn-2;X100=-X97=X94=...=X4=-X1=-a;X99=-X96=X93=...=X3X98=-X95=X92=...=X2S100=X1+X2+X3+...+X100=X2+X3+(X100+X1)+(X99+X6)+(x98+X5)+(X97+X4)+...+(X52+X49)+(X54+X51)+(X53+X50)=b+b-a=2b-a答案是A