已知公比q小于零的等比数列,s4=-20,s8=-1640.求an

已知公比q小于零的等比数列,s4=-20,s8=-1640.求an
已知公比q小于零的等比数列,s4=-20,s8=-1640.求an

已知公比q小于零的等比数列,s4=-20,s8=-1640.求an
设s=a1(1-q^n)/(1-q),
则s4=a1(1-q^4)/(1-q)=-20
s8=a1(1-q^8)/(1-q)=-1640
s4/s8=(1-q^4)/(1-q^8)=1/82
(1+q^4)=82
q=3,或q=-3
a1=-1/2 或a1=1,由题意可知q＜0,则q=-3,然后带入等比数列公式既可!希望采纳哦!

q<0
Sn= a1(q^n -1)/(q-1)
S8/S4= (q^8 -1)/(q^4 -1) = 82
q^4 +1=82
q^4 =81=3^4
q= - 3 (已知q<0)
S4=a1(q^4 -1 ) /(q-1) = -20a1 =-20 , a1=1
an=a1*q^(n-1) = (-3)^(n-1)