Question

设数列{an}的前n项和为Sn,点列(an,sn)在函数y=4096-x的图像上.求数列an

Answer 1

Sn=4096-an

Sn-1=4096-an-1

1式-2式,得

Sn-Sn-1=-an+an-1

则an=-an+an-1

则2an=an-1

an/an-1=1/2

所以数列{an}是以a1为首项1/2为公比的等比数列

an=2048*（1/2）^n-1