设等差数列{an}的首项a1及公差d都为整数,前n项和为sn.若a1>=6,a11>0,s14

题目

设等差数列{an}的首项a1及公差d都为整数,前n项和为sn.若a1>=6,a11>0,s14

答案

a1≥6 a11=a1+10d>0 s14=14a1+(14-1)*14d/2=14a1+91d≤77 a1≥6 a1>-10d a1≤(11-13d)/2 (11-13d)/2≥6 (11-13d)/2>-10d d≤(11-2*6)/13=-1/13 d>11/(13-20)=-11/7 -11/710 a1≤12 得出10