设{an}是等差数列,bn={1/2}^an,已知b1+b2+b3=21/8,b1b2b3=1/8,证明{bn}是等比数
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设{an}是等差数列,bn={1/2}^an,已知b1+b2+b3=21/8,b1b2b3=1/8,证明{bn}是等比数列
![设{an}是等差数列,bn={1/2}^an,已知b1+b2+b3=21/8,b1b2b3=1/8,证明{bn}是等比数](/uploads/image/z/3616569-9-9.jpg?t=%E8%AE%BE%7Ban%7D%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2Cbn%3D%7B1%2F2%7D%5Ean%2C%E5%B7%B2%E7%9F%A5b1%2Bb2%2Bb3%3D21%2F8%2Cb1b2b3%3D1%2F8%2C%E8%AF%81%E6%98%8E%7Bbn%7D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0)
(1/2)^a1+(1/2)^a2+(1/2)a^3=21/8
(1/2)^a1*(1/2)^a2*(1/2)^a3=1/8
(1/2)^(a1+a2+a3)=1/8
a2=1
a1=1或a1=4
a3=4或1
q=2或1/2
所以{bn}是等比数列
(1/2)^a1*(1/2)^a2*(1/2)^a3=1/8
(1/2)^(a1+a2+a3)=1/8
a2=1
a1=1或a1=4
a3=4或1
q=2或1/2
所以{bn}是等比数列
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