A3=2,A7=1有事数列{1\(AN+1)}等比数列则AN=

A3=2,A7=1有事数列{1\(AN+1)}等比数列则AN=
A3=2,A7=1有事数列{1\(AN+1)}等比数列则AN=

A3=2,A7=1有事数列{1\(AN+1)}等比数列则AN=
1/(an+1)是等比数列
令bn=1/(an+1)
所以b7=b3*q^4
所以1/(1+1)=q^4*1/(2+1)
q^4=3/2
q^2=√6/2
q=(3/2)^(1/4)或-(3/2)^(1/4)
所以1/(an+1)=bn=b3*q^(n-3)=1/(2+1)*[±(3/2)^(1/4)]^(n-3)
an=3/[±(3/2)^(1/4)]^(n-3)-1