Question

已知等差数列{an}的前四项和为2,前9项和为-6,求它的前n项和

Answer 1

因为

sn=a1*n+n(n-1)d/2

所以

s4=a1*4+4*3*d/2=2

2a1+3d=1 (1)

s9=a1*9+9*8*d/2=-6

3a1+12d=-2 (2)

(1)*4-(2)得

5a1=6

a1=6/5

d=-7/15

所以

sn=6/5*n+n(n-1)*(-7/30)