题目内容
如果a1,a2,a8为各项都大于零的等差数列,公差d≠0,则
- A.a1·a8>a4·a5
- B.a1·a8<a4·a5
- C.a1+a8>a4+a5
- D.a1·a8=a4·a5
B
a8=a1+7d,a4=a1+3d,a5=a1+4d,∴a1·a8=a21+a1·7d=a21+7a1d,a4·a5=(a1+3d)(a1+4d)=a21+7a1d+12d2.又∵d≠0,∴d2>0,
∴a1·a8<a4·a5
a8=a1+7d,a4=a1+3d,a5=a1+4d,∴a1·a8=a21+a1·7d=a21+7a1d,a4·a5=(a1+3d)(a1+4d)=a21+7a1d+12d2.又∵d≠0,∴d2>0,
∴a1·a8<a4·a5
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