如果公比q=1,3a1=-3/5,6a1=21/5
不可能,所以q不等于1
所以:
S3=a1(1-q^3)/(1-q)=-3/5
S6=a1(1-q^6)/(1-q)=21/5
所以(1-q^3)/(1-q^6)=-1/7
设q^3=m,所以(1-m)/(1-m^2)=-1/7
7m-7=1-m^2
m^2+7m-8=0
m=1(舌)或-8
所以q=-2
S3=a1(1+8)/(1+2)=-3/5, 所以a1=-1/5
所以该数列为:
-1/5, 2/5,-4/5,8/5,-16/5,32/5,-64/5,128/5,-256/5,512/5,...