设公比为q,数列各项均为正,则q>0
a3²=9a2·a6
(a1q²)²=9(a1q)(a1q^5)
a1²q^4=9a1²q^6
9q²=1
q²=1/9
q>0 q=1/3
2a1+3a2=1
2a1+3a1q=1
q=1/3代入,整理,得3a1=1
a1=1/3
an=a1q^(n-1)=(1/3)(1/3)^(n-1)=1/3ⁿ
数列{an}的通项公式为an=1/3ⁿ