等比数列{An}的前n项和为Sn，已知S1.S3.S2成等差数列 1，求{An}的公比q 2.求a1－a2=3,求Sn

显示全部楼层 · 2011-9-29 16:26:32

（1）S1.S3.S2成等差数列
则公差d=S3-S1=a2+a3
=S2-S3=-a2于是a2+a3=-a2,a3/a2=-2{an}为等比数列，则q=-2（2）a1－a2=a1-a1*q=3a1=3
a1=1Sn=a1*(1-q^n)/(1-q)
=[1-(-2)^n]/[1-(-2)]
=[1-(-2)^n]/3...

千问 · 2011-9-29 16:26:32

S1=a1S2=a1(1+q)S3=a1(1+q+q^2)S1,S3,S2成等差数列即s3-s1=s2-s31+q+q^2-1=1+q-(1+q+q^2)q^2+q=-q^2q=0（舍去）或-1/2a1(1-1/4)=3a1=4所以Sn=4*(1-(-1/2)^n)/(3/2)=8*(1-(-1/2)^n)/3...

千问 · 2011-9-29 16:26:32

(1)S3-S1=S2-S3a1+a2+a3-a1=a1+a2-a1-a2-a3a2+2a3=0 a2+2a2q=0
q=-1/2(2)a1-a3=3 a1-a1/4=3
a1=4Sn=a1(1-q^n)/(1-q)=4[1-(-1/2)^n]/(3/2)=8[1-(-1/2)^n]/3...

千问 · 2011-9-29 16:26:32

1）S1.S3.S2成等差数列
则公差d=S3-S1=a2+a3
=S2-S3=-a3于是a2+a3=-a2,a3/a2=-1/2{an}为等比数列，则q=-1/2（2）a1－a2=a1-a1*q=3a1=3
a1=1Sn=a1*(1-q^n)/(1-q)
=[1-(-...