Question

等比数列A,-6,B,-54,……的前n项和Sn等于?

Answer 1

设公比为q

则a2=a1*q=-6 (1)

a4=a1*q^3=-54 (2)

(2)/(1) q²=-54/(-6)=9

解得q=±3

分别代入(1) a1=A=-2或2

[1] a1=A=-2 q=3时

Sn=a1*(q^n-1)/(q-1)=-2*(3^n-1)/(3-1)=1-3^n

[2] a1=A=2 q=-3时

Sn=a1*(q^n-1)/(q-1)=2*[(-3)^n-1]/(-3-1)=(1/2)[1-(-3)^n]