设等比数列(an},若S3+S6=2S9,求证:a2,a8,a5成等差数列
问题描述：
设等比数列(an},若S3+S6=2S9,求证:a2,a8,a5成等差数列
答
证：S3+S6=2S9a1(q^3-1)/(q-1)+a1(q^6-1)/(q-1)=2a1(q^9-1)/(q-1)q^3-1+q^6-1=2q^9-2q^3+q^6=2q^92q^6-q^3-1=0(q^3-1)(2q^3+1)=0q^3=1或q^3=-1/2q^3=1时a2+a5=a1q+a1q^4=a1q(1+q^3)=2a1q2a8=2a1q^7=2a1q2a8=a2+a5a2,...