已知数列{an}是公差不为0的等差数列,若a5,a10,a20三项成等比数列,则此等比数列的公比为_.

问题描述:

已知数列{an}是公差不为0的等差数列,若a5,a10,a20三项成等比数列,则此等比数列的公比为______.

设数列{an}是公差为d,且d≠0,
因为a5,a10,a20三项成等比数列,
所以(a1+9d)2=(a1+4d)(a1+19d),
整理得5a1d=5d2,解得d=a1
则公比q=

a10
a5
=
a1+9d
a1+4d
=2,
故答案为:2.