已知等差数列{an}的前n项和为Sn,若S10=35,S22=473,求Sn在等差数列{an}中,（1）a1=105,an=994,d=7,求Sn(2)a1=1,an=-512,Sn=-1022,求d

Question

已知等差数列{an}的前n项和为Sn,若S10=35,S22=473,求Sn
在等差数列{an}中,
（1）a1=105,an=994,d=7,求Sn
(2)a1=1,an=-512,Sn=-1022,求d

Answer 1

设an=a1+(n-1)d Sn=n(a1+an)/2=na1+n(n-1)d/2
S10=10a1+45d=35
S22=22a1+231d=473
联立两式得a1=-10 d=3
Sn=-10n+3n(n-1)/2
(1)an-a1=(n-1)d
n=128
Sn=n(a1+an)/2=70336
(2)Sn=n(a1+an)/2
n=4
an=a1+(n-1)d
d=-171