已知等比数列an前n项和为Sn,S4=－20,S8=－1640,求a1和q

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

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

设s=a1(1-q^n)/(1-q),则s4=a1(1-q^4)=-20 s4=a1(1-q^8)=-1640 a1=1/2 q=3(或q=-3 a1=1)