等差数列An的前n项和为Sn,且S5=a4,若A4不等于0,则A7/A4=?

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等差数列An的前n项和为Sn,且S5=a4,若A4不等于0,则A7/A4=?
等差数列An的前n项和为Sn,且S5=a4,若A4不等于0,则A7/A4=?

等差数列An的前n项和为Sn,且S5=a4,若A4不等于0,则A7/A4=?
A(n) = a + r(n-1),n = 1,2,...
S(n) = na + rn(n-1)/2.
a + 3r = a(4) = S(5) = 5a + r5*4/2 = 5a + 10r,0=4a + 7r,a = -7r/4.
A(4)=a+3r=-7r/4+3r = 5r/4 不等于0,因此,r不等于0.
A(7)/A(4) = [a + 6r]/[a+3r] = [-7r/4 + 6r]/[-7r/4 + 3r] = 17/5

5a3=A4=A3+D,D=4A3
A3+4D/A3+D=17/5

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