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

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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
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

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
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)] = (d/2)[n^2 + n] = n(n+1)d/2
s(3)/s(7) = [3*4d/2]/[7*8d/2] = 3*4/(7*8) = 3/14

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