An=(lgB1+lgB2+……+lgBn)/n
n×An=lg(B1×B2×……×Bn)
B1×B2×……×Bn=10^(nAn)
B1×B2×……×B(n-1)=10^[(n-1)A(n-1)]
两式相除
Bn=10^[nAn-(n-1)A(n-1)]
=10^[n(An-A(n-1)+A(n-1)]
=10^[A(n-1)+nd]
=10^A(2n-1)
B1=10^(1×A1)=10^A1也满足上式
Bn/B(n-1)
=10^A(2n-1)/10^A(2n-3)
=10^[A(2n-1)-A(2n-3)]
=10^(2d)是定值
∴{Bn}是等比数列