公差不为零的等差数列(an)中,a2,a3,a6成等比数列,则其公比q为_____要求(详细过程)
问题描述:
公差不为零的等差数列(an)中,a2,a3,a6成等比数列,则其公比q为_____要求(详细过程)
答
等比则a3²=a2a6
(a1+2d)²=(a1+d)(a1+5d)
a1²+4a1d+4d²=a1²+6a1d+5d²
2a1d+d²=0
d≠0
d=-2a1
所以q=a3/a2
=(a1+2d)/(a1+3d)
=-3a1/(-5a1)
=3/5