已知数列{an}的前n项和Sn=n^2-9n,第k项满足5＜ak＜8,则k等于_数学解答

已知数列{an}的前n项和Sn=n^2-9n,第k项满足5＜ak＜8,则k等于

人气：392 ℃　时间：2020-03-25 07:17:49

解答

Sn=n^2-9nS(n-1)=(n-1)^2-9(n-1)=n^2-2n+1-9n+9=n^2-11n+10an=Sn-S(n-1)=n^2-9n-(n^2-11n+10)=n^2-9n-n^2+11n-10=2n-10ak=2k-105＜ak＜85＜2k-10＜815＜2k＜187.5＜k＜9所以k=8