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 ,
a3, 2a2成等差数列,则公比q=______. 1 2
答
∵an为等比数列且由已知a1 ,
a3, 2a2得a1q2=a1+2a1q (a1>0)⇒q2=1+2q⇒q=1+1 2
或q=1−
2
(舍)
2
故答案为:1+
2