题目

已知等差数列{an}的公差d不等于0,其前n项和为sn,且a1,a3,a9成等比数列,则s3/s7=多少

提问时间：2021-03-14

答案

a(n) = a + (n-1)d,d不为0.[a(3)]^2 = a(1)a(9) = a[a+8d] = [a+2d]^2,0 = a^2 + 8ad - a^2 - 4ad - 4d^2 = 4ad - 4d^2 = 4d(a-d),0 = a-d.a = d.a(n) = d + (n-1)d,s(n) = nd + n(n-1)d/2 = (d/2)[2n + n(n-1)] = (...