已知等比数列an前n项和为Sn,S4=－20,S8=－1640,求a1和q
问题描述：
已知等比数列an前n项和为Sn,S4=－20,S8=－1640,求a1和q
答
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