设a1,d为实数,首项为a1,公差为d的等差数列an的前n项和为sn,满足s5s6+15=0,若s5=15

问题描述:

设a1,d为实数,首项为a1,公差为d的等差数列an的前n项和为sn,满足s5s6+15=0,若s5=15

s5=15,则 s5s6+15=15s6+15=15(s6+1)=0,那么s6+1=0,s6=-1.
s5=5a1+10d=15
s6=6a1+15d=-1
由以上2式解得
a1和d
a1=47/3
d=-19/3
s6=-3
a1=7