问题
填空题
等比数列{an}的前n项和为Sn,且2Sn=Sn+1+Sn+2,则公比q=______.
答案
∵2Sn=Sn+1+Sn+2
∴2Sn=Sn+a1qn+Sn+a1qn+a1qnq,即2a1qn+a1qn+1=0
∵数列{an}为等比数列
∴a1≠0,q≠0
∴2+q=0
∴q=-2
故答案为-2
等比数列{an}的前n项和为Sn,且2Sn=Sn+1+Sn+2,则公比q=______.
∵2Sn=Sn+1+Sn+2
∴2Sn=Sn+a1qn+Sn+a1qn+a1qnq,即2a1qn+a1qn+1=0
∵数列{an}为等比数列
∴a1≠0,q≠0
∴2+q=0
∴q=-2
故答案为-2