证：
由lga1,lga2,lga4成等差数列,得
2lga2=lga1+lga4
lg(a2)²=lg(a1a4)
a2²=a1a4
(a1+d)²=a1(a1+3d)
整理,得
d(a1-d)=0
d=0或a1=d
d=0时,an=a1
bn=1/a(2n)=1/a1,为定值,数列{bn}是以1/a1为首项,1为公比的等比数列.
a1=d时,a2n=a1+(2n-1)d=a1+2na1-a1=2na1
bn=1/a(2n)=1/2na1
bn-1=1/[2(n-1)a1]
bn/b(n-1)=n/(n-1),不是定值.数列不是等比数列,题目有问题.