已知等比数列{an}中,各项都是正数,且a1 ,1/2a3, 2a2成等差数列,则公比q=_.

问题描述:

已知等比数列{an}中,各项都是正数,且a1 ,

1
2
a3, 2a2成等差数列,则公比q=______.

∵an为等比数列且由已知a1 ,

1
2
a3, 2a2得a1q2=a1+2a1q (a1>0)⇒q2=1+2q⇒q=1+
2
q=1−
2
 (舍) 
故答案为:1+
2