已知数列{xn}满足xn+1=xn-xn-1(n≥2),x1=a,x2=b,记Sn=x1+x2+…+xn.则下列结论正确的是(A) x100= -a ,S100=2b-a;(B) x100= -b ,S100=2b-a;(C) x100= -b ,S100=b-a;(D) x100=-a ,S100=b-a;
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![已知数列{xn}满足xn+1=xn-xn-1(n≥2),x1=a,x2=b,记Sn=x1+x2+…+xn.则下列结论正确的是(A) x100= -a ,S100=2b-a;(B) x100= -b ,S100=2b-a;(C) x100= -b ,S100=b-a;(D) x100=-a ,S100=b-a;](/uploads/image/z/1324529-17-9.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Bxn%7D%E6%BB%A1%E8%B6%B3xn%2B1%3Dxn-xn-1%28n%E2%89%A52%29%2Cx1%3Da%2Cx2%3Db%2C%E8%AE%B0Sn%3Dx1%2Bx2%2B%E2%80%A6%2Bxn.%E5%88%99%E4%B8%8B%E5%88%97%E7%BB%93%E8%AE%BA%E6%AD%A3%E7%A1%AE%E7%9A%84%E6%98%AF%EF%BC%88A%EF%BC%89+x100%3D+-a+%2CS100%3D2b-a%3B%EF%BC%88B%EF%BC%89+x100%3D+-b+%2CS100%3D2b-a%3B%EF%BC%88C%EF%BC%89+x100%3D+-b+%2CS100%3Db-a%3B%EF%BC%88D%EF%BC%89+x100%3D-a+%2CS100%3Db-a%3B)
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已知数列{xn}满足xn+1=xn-xn-1(n≥2),x1=a,x2=b,记Sn=x1+x2+…+xn.则下列结论正确的是(A) x100= -a ,S100=2b-a;(B) x100= -b ,S100=2b-a;(C) x100= -b ,S100=b-a;(D) x100=-a ,S100=b-a;
已知数列{xn}满足xn+1=xn-xn-1(n≥2),x1=a,x2=b,记Sn=x1+x2+…+xn.则下列结论正确的是
(A) x100= -a ,S100=2b-a;
(B) x100= -b ,S100=2b-a;
(C) x100= -b ,S100=b-a;
(D) x100=-a ,S100=b-a;
已知数列{xn}满足xn+1=xn-xn-1(n≥2),x1=a,x2=b,记Sn=x1+x2+…+xn.则下列结论正确的是(A) x100= -a ,S100=2b-a;(B) x100= -b ,S100=2b-a;(C) x100= -b ,S100=b-a;(D) x100=-a ,S100=b-a;
x1=a
x2=b
x3=x2-x1=b-a
x4=x3-x2=-a
x5=x4-x3=-b
x6=x5-x4=a-b
x7=x6-x5=a
所以这个数列是循环的,100除以6余4所以x100=x4=-a
S6=S12=...=96=0
S100=S96+x97+x98+x99+x100=x1+x2+x3+x4=2b-a
选A,一般这种特别离奇的数列都是循环的,不然就没法做了.
答案是A
你仔细看看就是了
不难啊
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