题目内容


a1a2a3a4是各项不为零的等差数列且公差d≠0,若将此数列删去某一项得到的数列(按原来的顺序)是等比数列,则的值为(  )

A.-4或1      B.1      C.4      D.4或-1


A [若删去a1,则a2a4a

即(a1d)(a1+3d)=(a1+2d)2,化简,得d=0,不合题意;

若删去a2,则a1a4a

a1(a1+3d)=(a1+2d)2,化简,得=-4;

若删去a3,则a1a4a

a1(a1+3d)=(a1d)2,化简,得=1;

若删去a4,则a1a3a

a1(a1+2d)=(a1d)2,化简,得d=0,不合题意.故选A.]


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