等比数列{an}的公比为q,前n项和为Sn,若Sn+1,Sn,Sn+2成等差数列,则,q的值为
问题描述：
等比数列{an}的公比为q,前n项和为Sn,若Sn+1,Sn,Sn+2成等差数列,则,q的值为
注意,是前n+1项,n项,n+2项,不是第多少项+1,答案是q=-2,我觉得1也可以
答
设an=a1q^(n-1)Sn=a1(1-q^n)/(1-q)Sn+1=a1(1-q^(n+1))/(1-q)Sn+2=a1(1-q^(n+2))/(1-q)根据题意有：Sn-Sn+1=（Sn+2）-Sn,整理得：q^2+q-2=0解得：q=－2或q=1当q=1时,等比数列蜕变为公差为0的等差数列,也满足题中要求....