Question

设等差数列{an}的前n项和为Sn,且S3=-51,S5=-70.求an和Sn

Answer 1

由S3=-51得a2=-17，又S5=-70得a3=-14，故等差数列an是以3为公差-20为首项的等差数列，故an=3n-23，Sn=(-43n+3n^2)/2

Answer 2

S3=3a2=-51
S5=5s3=-70
a2=-17,a3=-14
an=-20+3(n-1)=3n-23
Sn=(a1+an)n/2=(3n-43)n/2

Answer 3

根据s3求出第二项，根据s5求出第四项。可求出a1,d则可求出an,sn

Answer 4

S3=3a(2),S5=5a(3)
a(2)=-17,a(3)=-14,
d=a(3)-a(2)=3
a(1)=-20
Sn=-20n+(n-1)n3/2

Answer 5

S3=3a2=-51
S5=5a3=-70
a2=-17,a3=-14
d=a3-a2=3
a1=a2-d=-20
an=-20+3(n-1)=3n-23
Sn=na1+n(n-1)d/2=-20n+3(n-1)n/2=(3n-43)n/2