等比数列{xn}各项为不为1的正数,数列{yn}满足yn=2log a Xn (a>0,不等于1),y4=17,y7=11证{yn}为等差数列《2》{yn}前多少项和最大,最大值是多少
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![等比数列{xn}各项为不为1的正数,数列{yn}满足yn=2log a Xn (a>0,不等于1),y4=17,y7=11证{yn}为等差数列《2》{yn}前多少项和最大,最大值是多少](/uploads/image/z/10460095-7-5.jpg?t=%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Bxn%7D%E5%90%84%E9%A1%B9%E4%B8%BA%E4%B8%8D%E4%B8%BA1%E7%9A%84%E6%AD%A3%E6%95%B0%2C%E6%95%B0%E5%88%97%7Byn%7D%E6%BB%A1%E8%B6%B3yn%3D2log+a+Xn+%28a%3E0%2C%E4%B8%8D%E7%AD%89%E4%BA%8E1%EF%BC%89%2Cy4%3D17%2Cy7%3D11%E8%AF%81%7Byn%7D%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E3%80%8A2%E3%80%8B%7Byn%7D%E5%89%8D%E5%A4%9A%E5%B0%91%E9%A1%B9%E5%92%8C%E6%9C%80%E5%A4%A7%2C%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF%E5%A4%9A%E5%B0%91)
等比数列{xn}各项为不为1的正数,数列{yn}满足yn=2log a Xn (a>0,不等于1),y4=17,y7=11证{yn}为等差数列《2》{yn}前多少项和最大,最大值是多少
等比数列{xn}各项为不为1的正数,数列{yn}满足yn=2log a Xn (a>0,不等于1),y4=17,y7=11
证{yn}为等差数列
《2》{yn}前多少项和最大,最大值是多少
等比数列{xn}各项为不为1的正数,数列{yn}满足yn=2log a Xn (a>0,不等于1),y4=17,y7=11证{yn}为等差数列《2》{yn}前多少项和最大,最大值是多少
假设X(1)=x,X(n)=xk^(n-1) (k>0,x>0,x≠1)
y4=2log a X4=2log a(xk^3)=2loga x+2loga k^3=2loga x+6loga k=17
y7=2log a X7=2log a(xk^6)=2loga x+2loga k^6=2loga x+12loga k=11
所以6loga k=-6
loga k=-1
2loga x =23
yn=2log a Xn =2log a [xk^(n-1)]
=2loga x + (n-1)2log a k
=2loga x -(2n-2)
=23-2n+2
=25-2n
yn-y(n-1)=25-2n-25+2(n-1)
=-2n+2n-2
=-2
所以等差,公差-2
(2) ym=0
25-2m=0
m=25/2
所以y13
(1)证:∵Yn-Yn-1=2logaXn-2logaXn-1
=2(logaXn-logaXn-1)
=2loga(Xn/Xn-1)
又数列{xn}为等比数列,
∴Xn/Xn-1=k—为一个常数
∴Yn-Yn-1=d—d为一个常数
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(1)证:∵Yn-Yn-1=2logaXn-2logaXn-1
=2(logaXn-logaXn-1)
=2loga(Xn/Xn-1)
又数列{xn}为等比数列,
∴Xn/Xn-1=k—为一个常数
∴Yn-Yn-1=d—d为一个常数
∴据等差数列定义可知,数列{yn}为等差数列,
且公差d=2loga(Xn/Xn-1)
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