设等差数列an的前n项和为sn,若1≤a5≤4,2≤a6≤3,则s6的取值范围是

设等差数列an的前n项和为sn,若1≤a5≤4,2≤a6≤3,则s6的取值范围是
设等差数列an的前n项和为sn,若1≤a5≤4,2≤a6≤3,则s6的取值范围是

设等差数列an的前n项和为sn,若1≤a5≤4,2≤a6≤3,则s6的取值范围是
a5=a1+4d,a6=a1+5d,
所以1≤a1+4d≤4,2≤a1+5d≤3,
所以-20≤-5a1-20d≤-5,6≤3a1+15d≤9,
两式相加得,-14≤-2a1-5d≤4,
两边同乘以-1,-4≤2a1+5d≤14.
两边同乘以3,-12≤6a1+15d≤42.
又因为S6=6a1+15d,所以-12≤S6≤42.