设数列{An}满足a1=2,An+1=入An+2^n,n属于N*,入为常数(1)若A2=0,求A3的值;(2)是否存在实数入,使得数列{An}为等差数列,若存在,求数列{An}的通项公式,若不存在,请说明理由;(3)设入=1,Bn=4n-7/An,
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 21:31:03
![设数列{An}满足a1=2,An+1=入An+2^n,n属于N*,入为常数(1)若A2=0,求A3的值;(2)是否存在实数入,使得数列{An}为等差数列,若存在,求数列{An}的通项公式,若不存在,请说明理由;(3)设入=1,Bn=4n-7/An,](/uploads/image/z/5561704-64-4.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3a1%3D2%2CAn%2B1%3D%E5%85%A5An%2B2%5En%2Cn%E5%B1%9E%E4%BA%8EN%2A%2C%E5%85%A5%E4%B8%BA%E5%B8%B8%E6%95%B0%EF%BC%881%EF%BC%89%E8%8B%A5A2%3D0%2C%E6%B1%82A3%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%882%EF%BC%89%E6%98%AF%E5%90%A6%E5%AD%98%E5%9C%A8%E5%AE%9E%E6%95%B0%E5%85%A5%2C%E4%BD%BF%E5%BE%97%E6%95%B0%E5%88%97%7BAn%7D%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E8%8B%A5%E5%AD%98%E5%9C%A8%2C%E6%B1%82%E6%95%B0%E5%88%97%7BAn%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%2C%E8%8B%A5%E4%B8%8D%E5%AD%98%E5%9C%A8%2C%E8%AF%B7%E8%AF%B4%E6%98%8E%E7%90%86%E7%94%B1%EF%BC%9B%EF%BC%883%EF%BC%89%E8%AE%BE%E5%85%A5%3D1%2CBn%3D4n-7%2FAn%2C)
设数列{An}满足a1=2,An+1=入An+2^n,n属于N*,入为常数(1)若A2=0,求A3的值;(2)是否存在实数入,使得数列{An}为等差数列,若存在,求数列{An}的通项公式,若不存在,请说明理由;(3)设入=1,Bn=4n-7/An,
设数列{An}满足a1=2,An+1=入An+2^n,n属于N*,入为常数
(1)若A2=0,求A3的值;
(2)是否存在实数入,使得数列{An}为等差数列,若存在,求数列{An}的通项公式,若不存在,请说明理由;
(3)设入=1,Bn=4n-7/An,数列{Bn}的前n 项和为Sn,求满足Sn>0的最小自然数n的值.
设数列{An}满足a1=2,An+1=入An+2^n,n属于N*,入为常数(1)若A2=0,求A3的值;(2)是否存在实数入,使得数列{An}为等差数列,若存在,求数列{An}的通项公式,若不存在,请说明理由;(3)设入=1,Bn=4n-7/An,
(1)
A1 = 2,A2 = 0
所以 λ = (0-2^1) / 2 = -1
所以A3 = -1x0 + 2^2 = 4
(2)
可以直接从前三项考虑
A1 = 2,A2 = 2λ+2,A3=λA2+4=2λ^2+2λ+4
若这三项为等差,则有A3 - A2 = A2 - A1
即有λ^2-λ+1=0,而△ = 1-4 = -3