设Sn是等比数列的前n项和,若S3,S9,S6成等差数列,这an的公比q为多少_百 ...答:S3=a1(1-q³)/(1-q),S9=a1(1-q^9)/(1-q),S6=a1(1-q^6)/(1-q),2S9=S3+S6, 2a1(1-q^9)/(1-q)=a1(1-q³)/(1-q)+a1(1-q^6)/(1-q),2q^9=q³+q^6,2q^6=1+q³,(q³-1)(2q³+1)=0 q³=1或q³=-1/...
设Sn是等比数列{an}的前n项和,S3,S9,S6,成等差数列,则公比q=?答:解:设第一项为a1,由等比数列{an}的前n项和公式得:Sn=[a1(1-q^n)]/(1-q).则:S3=[a1(1-q^3)]/(1-q);S6=[a1(1-q^6)]/(1-q);S9=[a1(1-q^9)]/(1-q)。又因为S3,S9,S6,成等差数列,所以 2*S9=S3+S6.代入整理后得:2q^9-q^6-q^3=0;设x=q^3,则上式为...