等差数列{an}的公差和等比数列{bn}的公比都是d,且a1=b1,a4=b4,a10=b10(1、4、10均为项数) 求a1和d

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等差数列{an}的公差和等比数列{bn}的公比都是d,且a1=b1,a4=b4,a10=b10(1、4、10均为项数) 求a1和d

an = a1 + (n-1)d bn = b1×d^(n-1) a1 = b1 a4 = b4 所以 a1+3d = b1*d^3 (1) a10 = b10 所以 a1+9d = b1*d^9 (2) 两式相减:6d = b1(d^3-d^9) a1=b1=6d/(d^3-d^9) 代入 (1)或(2) a1=2^(1/3) d=-2^(1/3)...