{an}为等差数列,若a11/a10

题目

{an}为等差数列,若a11/a10

答案

an=bn+c
Sn=(a1+an)*n/2=(b+c+bn+c)*n/2=n(b+bn+2c)/2有最小值
得b>0,{an}为等差增数列
∵a11/a10<-1,得a11>-a10>0>a10
11b+c>-10b-c>10b+c
21b+2c>0>10b+c,11b+c>21b+2c>0
当Sn=n(b+bn+2c)/2>0,b+bn+2c>0
当n=19时,Sn=20b+2c<0,当n=20时,Sn=21b+2c>0,
∴得n最小为20