已知公差不为零的等差数列{an}中,sn是其前n项,且s1,s2,s4成等比数列求数列s1,s2,s4的公比q

问题描述:

已知公差不为零的等差数列{an}中,sn是其前n项,且s1,s2,s4成等比数列
求数列s1,s2,s4的公比q

s1 = a1s2 = 2a1 + ds4 = 4a1 + 6d因为s1,s2,s4成等比数列所以 (s2)² = s1×s4(2a1 + d)² = a1(4a1 + 6d)4a1² + 4a1d + d² = 4a1² + 6a1dd² = 2a1d因为 d ≠ 0所以 d = 2a1所以 s2 = ...