等差数列an中,a1=2,公差d≠0,且a1,a3,a11恰好是某等比数列的前三项,那么该等比数列的公比是?
问题描述:
等差数列an中,a1=2,公差d≠0,且a1,a3,a11恰好是某等比数列的前三项,那么该等比数列的公比是?
答
a3²=a1a11
(a1+2d)²=a1(a1+10d)
a1²+4a1d+4d²=a1²+10a1d
4d²=6a1d
a1=2d/3
所以q= a3/a1
=(a1+2d)/a1
=4q为什么= a3/a1a1,a3,a11等比