等比数列{An}前4项的和为-45,前6项的和为-189,求SnAn=3-3*(土2)的n次

Question

等比数列{An}前4项的和为-45,前6项的和为-189,求Sn
An=3-3*(土2)的n次

Answer 1

a1(1-q^4)/(1-q)=-45
a1(1-q^6)/(1-q)=-189
q=-2,a1=9,Sn=3(1-(-2)^n)
或q=2,a1=-3,Sn=3(1-2^n)
设a1+a2==a1+a1q=b
b+bq^2=-45
bq^4=-144
解得q^2=4,b=-9
q=2,a1=-3
q=-2,a1=9