设数列{an}是等差数列,公差d≠0;{bn}是等比数列,公比q≠1,若a3=b6,a6=b8,a14=b10,则等比数
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设数列{an}是等差数列,公差d≠0;{bn}是等比数列,公比q≠1,若a3=b6,a6=b8,a14=b10,则等比数列{bn}公比
a3=b6 a6=b8 a14=b10
a6/a3=b8/b6=q² a14/a6=b10/b8=q²
a6/a3=a14/a6
a3a14=a6²
(a1+2d)(a1+13d)=(a1+5d)²
整理,得
d²+5a1d=0
d(d+5a1)=0
d=0(舍去)或d=-5a1
q²=a6/a3=(a1+5d)/(a1+2d)=(a1-25a1)/(a1-10a1)=24/9
q=2√6/3或q=-2√6/3
a6/a3=b8/b6=q² a14/a6=b10/b8=q²
a6/a3=a14/a6
a3a14=a6²
(a1+2d)(a1+13d)=(a1+5d)²
整理,得
d²+5a1d=0
d(d+5a1)=0
d=0(舍去)或d=-5a1
q²=a6/a3=(a1+5d)/(a1+2d)=(a1-25a1)/(a1-10a1)=24/9
q=2√6/3或q=-2√6/3
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