Question

等差数列｛a n｝中,前N项和为Sn,首项a1＝4,S9＝0,求公差d,若an+sn=－10,求n

Answer 1

S9=9a1+36d=36+36d=0.

所以,d=-1.

an=a1+(n-1)d=4-n+1=5-n.

Sn=na1+n(n-1)d/2=4n-(1/2)(n^2-n)=-(1/2)n^2+(9/2)n.

an+Sn=-(1/2)n^2+(7/2)n+5=-10.

整理得：n^2-7n-30=0.

解得：n=-3(舍去)、n=10.