高一等比数列试题1.已知等差数列{an}的公差和等比数列{bn}的工笔都是d,又知d不等于0,且a1=b1,a4=b4,a10=b10.(1)求a1及d的值 (2)b16是不是{an}中的项
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![高一等比数列试题1.已知等差数列{an}的公差和等比数列{bn}的工笔都是d,又知d不等于0,且a1=b1,a4=b4,a10=b10.(1)求a1及d的值 (2)b16是不是{an}中的项](/uploads/image/z/8035991-71-1.jpg?t=%E9%AB%98%E4%B8%80%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%E8%AF%95%E9%A2%981.%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%85%AC%E5%B7%AE%E5%92%8C%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%B7%A5%E7%AC%94%E9%83%BD%E6%98%AFd%2C%E5%8F%88%E7%9F%A5d%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E4%B8%94a1%3Db1%2Ca4%3Db4%2Ca10%3Db10.%281%29%E6%B1%82a1%E5%8F%8Ad%E7%9A%84%E5%80%BC+%282%29b16%E6%98%AF%E4%B8%8D%E6%98%AF%7Ban%7D%E4%B8%AD%E7%9A%84%E9%A1%B9)
高一等比数列试题1.已知等差数列{an}的公差和等比数列{bn}的工笔都是d,又知d不等于0,且a1=b1,a4=b4,a10=b10.(1)求a1及d的值 (2)b16是不是{an}中的项
高一等比数列试题
1.已知等差数列{an}的公差和等比数列{bn}的工笔都是d,又知d不等于0,且a1=b1,a4=b4,a10=b10.
(1)求a1及d的值
(2)b16是不是{an}中的项
高一等比数列试题1.已知等差数列{an}的公差和等比数列{bn}的工笔都是d,又知d不等于0,且a1=b1,a4=b4,a10=b10.(1)求a1及d的值 (2)b16是不是{an}中的项
a(1)=b(1)=a,
a(n)=a+(n-1)d,b(n)=ad^(n-1).
a(4)=a+3d=b(4)=ad^3,3d=a[d^3-1],d不为0,因此,d不为1.
a=3d/[d^3-1].
a(10)=a+9d=b(10)=ad^9,
3d/[d^3-1] + 9d = 3d^(10)/[d^3-1],
3d + 9d[d^3-1] = 3d^(10),
1 + 3[d^3-1] = d^9,
0=d^9 - 3d^3 + 2=d^9 - d^6 + d^6 - d^3 - 2d^3 + 2 = d^6[d^3-1] + d^3[d^3-1] - 2[d^3-1],
d不为1,
0=d^6 + d^3 - 2 = [d^3+2][d^3-1],
d^3 = -2.d^3-1 = -3.d=(-2)^(1/3).
a=3d/[d^3-1]=-d=2^(1/3).
a(1)=a=2^(1/3),d = -2^(1/3).
b(16)=ad^(15)=a(-2)^5=-32a=a-33a=a+33d=a(34)
b(16)是{a(n)}中的第34项.
他做的太烦啦!