已知数列{an}的通元an=3n+1,求证:1、{an}是等差数列;2、若bn=pan+q(pq为常数)求证:﹛bn﹜也是等差数列
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 03:17:08
![已知数列{an}的通元an=3n+1,求证:1、{an}是等差数列;2、若bn=pan+q(pq为常数)求证:﹛bn﹜也是等差数列](/uploads/image/z/5257176-24-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E9%80%9A%E5%85%83an%3D3n%2B1%2C%E6%B1%82%E8%AF%81%3A1%E3%80%81%EF%BD%9Ban%EF%BD%9D%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%EF%BC%9B2%E3%80%81%E8%8B%A5bn%3Dpan%2Bq%28pq%E4%B8%BA%E5%B8%B8%E6%95%B0%29%E6%B1%82%E8%AF%81%EF%BC%9A%EF%B9%9Bbn%EF%B9%9C%E4%B9%9F%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97)
已知数列{an}的通元an=3n+1,求证:1、{an}是等差数列;2、若bn=pan+q(pq为常数)求证:﹛bn﹜也是等差数列
已知数列{an}的通元an=3n+1,求证:1、{an}是等差数列;2、若bn=pan+q(pq为常数)求证:
﹛bn﹜也是等差数列
已知数列{an}的通元an=3n+1,求证:1、{an}是等差数列;2、若bn=pan+q(pq为常数)求证:﹛bn﹜也是等差数列
a[n+1]=3(n+1)+1=3n+4
a[n+1]-an =3n+4-(3n+1)=3
所以an是等差数列
bn=p(3n+1)+q
b[n+1]=p(3n+4)+q
b[n+1]-bn=p(3n+4)-p(3n+1)=3p
得证