题目内容
a1,a2,a3,a4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a2a4=a
,
即(a1+d)(a1+3d)=(a1+2d)2,化简,得d=0,不合题意;
若删去a2,则a1a4=a
,
即a1(a1+3d)=(a1+2d)2,化简,得
=-4;
若删去a3,则a1a4=a
,
即a1(a1+3d)=(a1+d)2,化简,得
=1;
若删去a4,则a1a3=a
,
即a1(a1+2d)=(a1+d)2,化简,得d=0,不合题意.故选A.]
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