等差数列【an】中,s4=2,s9=-6,求sn

题目

等差数列【an】中,s4=2,s9=-6,求sn

答案

s9-s4=a5+a6+a7+a8+a9=5a7=-8==>a7=-8/5,s9=9*(a1+a9)/2=9a5=-6==>a5=-2/3,d=(a7-a5)/2=(-8/5+2/3)/2=-7/15,a1=a5-4d=-2/3+4*7/15=6/5 sn=-7n^2/30+43n/30