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

题目

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

答案

(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