Question

等比数列{an}的前n项和为Sn已知对任意的n属于N+ 点（n，Sn）均在函数y=b的x方+r 1.求r的值

当b=2时 记Bn=n+1/4an 求数列bn的前n项和Tn

Answer 1

点（n，Sn）均在函数y=b的x方+r

1.Sn=b^n+r,a1=S1=b+r,S2=a1+a2=b^2+r,a2=b^2-b,

S3=a1+a2+a3=b^3+r,a3=b^3-b^2,等比数列{an},a2^2=a1*a3,r=-1

2. b=2,an=2^(n-1)

Bn=n+1/4an =n+1/2^(n+1),等差+等比，分别求和

Tn =(1+n)*n/2+1/2*[1-(1/2)^n]

Answer 2

设数列{an}首项为a1,有题目条件知 y=b^n+r=a1(1-q^n)/(1-q)
代入n=1 得b+r=a1
代入n=2 得b^2+r=a1(1+q)
代入n=3 嘚b^3+r=a1(1+q+q^2)
连立得 a1=b+r q=(b^2-b)/(b+r)