已知等比数列an各项为实数,且公比为q,前n项和为Sn,且S3,S6,S9成等差数列,（1）求q的值;(2)求证:a2、a8、a5成等差数列

(1)设等比数列{an}的公比为qS3,S6,S9成等差数列那么2S6=S3+S9当q=1时,Sn=na1∴12a1=3a1+9a1,符合题意当q≠1时,那么2a1(q^6-1)/(q-1)=a1(q^3-1)/(q-1)+a1(q^9-1)/(q-1)2q^6-2=q^3-1+q^9-1q^9-2q^6+q^3=0约掉q^3q^6-2q...