已知等差数列{an}中,公差d>0,其前n项和为Sn,且满足:a2*a3=45,a1+a4=14(1)求数列{an}通项公式(2)通过公式Bn=Sn/(n+c)构造一个新数列{Bn}.若{Bn}也是等差数列,求非零常数c(3)求f(n)=Bn/[(n+25)*
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![已知等差数列{an}中,公差d>0,其前n项和为Sn,且满足:a2*a3=45,a1+a4=14(1)求数列{an}通项公式(2)通过公式Bn=Sn/(n+c)构造一个新数列{Bn}.若{Bn}也是等差数列,求非零常数c(3)求f(n)=Bn/[(n+25)*](/uploads/image/z/645358-22-8.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2C%E5%85%AC%E5%B7%AEd%3E0%2C%E5%85%B6%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E4%B8%94%E6%BB%A1%E8%B6%B3%3Aa2%2Aa3%3D45%2Ca1%2Ba4%3D14%EF%BC%881%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%882%EF%BC%89%E9%80%9A%E8%BF%87%E5%85%AC%E5%BC%8FBn%3DSn%2F%EF%BC%88n%2Bc%EF%BC%89%E6%9E%84%E9%80%A0%E4%B8%80%E4%B8%AA%E6%96%B0%E6%95%B0%E5%88%97%7BBn%7D.%E8%8B%A5%7BBn%7D%E4%B9%9F%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E6%B1%82%E9%9D%9E%E9%9B%B6%E5%B8%B8%E6%95%B0c%EF%BC%883%EF%BC%89%E6%B1%82f%EF%BC%88n%EF%BC%89%3DBn%2F%5B%EF%BC%88n%2B25%EF%BC%89%2A)
已知等差数列{an}中,公差d>0,其前n项和为Sn,且满足:a2*a3=45,a1+a4=14(1)求数列{an}通项公式(2)通过公式Bn=Sn/(n+c)构造一个新数列{Bn}.若{Bn}也是等差数列,求非零常数c(3)求f(n)=Bn/[(n+25)*
已知等差数列{an}中,公差d>0,其前n项和为Sn,且满足:a2*a3=45,a1+a4=14
(1)求数列{an}通项公式
(2)通过公式Bn=Sn/(n+c)构造一个新数列{Bn}.若{Bn}也是等差数列,求非零常数c
(3)求f(n)=Bn/[(n+25)*B(n+1)]的最大值
已知等差数列{an}中,公差d>0,其前n项和为Sn,且满足:a2*a3=45,a1+a4=14(1)求数列{an}通项公式(2)通过公式Bn=Sn/(n+c)构造一个新数列{Bn}.若{Bn}也是等差数列,求非零常数c(3)求f(n)=Bn/[(n+25)*
因为是等差数列,
所以,a1+a4=a3+a2=14
所以a3=14-a2,
将a3=14-a2代入a2a3=45得
(14-a2)*a2=45
a2^2-14a2+45=0
(a2-5)(a2-9)=0
a2=5或a2=9
a3=14-a2=14-5=9或a3=14-a2=14-9=5
d=a3-a2=9-5=4或d=a3-a2=5-9=-4(公差d>0,舍去)
所以,d=4
a1=a2-d=5-4=1
an=1+(n-1)*4=4n-3
(2)sn=n(a1+an)/2
Bn=Sn/(n+c)
Bn=n(a1+an)/[2(n+c)]
b1=1/(2+2c)
b2=2(1+5)/[2(2+c)]=6/(2+c)
b3=3(1+9)/[2(3+c)]=15/(3+c)
2b2=b1+b3
2*6/(2+c)=15/(3+c)+1/(2+2c)
12/(2+c)=15/(3+c)+1/(2+2c)