Question

①a1=20,an=54,Sn=999,求d及n ②d=1/3,n=37,Sn=629,求a1及a

Answer 1

(1)Sn=n(a1+an)/2,把a1=20,an=54,Sn=999代入得到

999=n(20+54)/2,所以n=27

因为an=a1+(n-1)d,所以54=20+(27-1)d

所以d=17/13

(2)a1 +36d=an

37a1+18*37=629

a1=-1 an=11

(3)5n/6-12n(n-1)=-5

(n-15)(n+4)=0

n=15 an =-7/6

(4)an=a1+(n-1)d,所以-10=a1+(15-1)*2

a1=-38

sn=n(a1+an)/2=15*(-38-10)/2=-360