Question

等差数列{an}中,S2=2,S3=-6,则an=？

Answer 1

解念乱纳：等差数列｛an｝仔没，s2＝2，s3＝-6，那么该数列首陪告项是a1、公差是d；
s2＝2a1＋2×（2-1）d／2＝2
2a1＋d＝2①
s3＝3a1＋3×（3-1）d／2＝-6，
3a1＋3d＝-6，a1＋d＝-2②
解得①与②，a1＝4，d＝-6
∴an＝a1＋（n-1）d＝10-6n
＜

Answer 2

an =a1+(n-1)d
S2 =2
2a1 +d =2 (1)
S3=-6
3a1+3d =-6
a1+d =-2 (2)
(1)-(2)
a1 =4
from (2)
a1+d =-2
4+d =-2
d=-6
an = 4-6(n-1) = -6n+10