Question

已知等比数列an前n项和为Sn,S4=－20,S8=－1640,求a1和q

Answer 1

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