已知在等差数列{an}中,a1=20,an=54,sn=999,求n与d

问题描述:

已知在等差数列{an}中,a1=20,an=54,sn=999,求n与d

an=a1+(n-1)d=54
sn=n(a1+an)/2=999
故n=27,d=34/26=17/13

(a1+an)n/2=999
(20+54)n/2=999
n=999*2/74=999/37=27
a1+(n-1)d=an
20+(27-1)d=54
d=34/(26)=17/13