题目

等比数列{an}的前n项和为Sn，若a1=3，S3=9，求数列{an}的公比与S10．                    答案：【分析】设等比数列{an}的公比为q，y由a1=3，S3=9，可得a1+a2+a3=3（1+q+q2）=9，解得q，利用求和公式即可得出．                                                                                     【解答】解：设等比数列{an}的公比为q，∵a1=3，S3=9，                                            ∴a1+a2+a3=3（1+q+q2）=9，化为：q2+q﹣2=0，解得q=1或﹣2．                                  q=1时，S10=30．                                                                                                 q=﹣2时，S10==﹣1023．                                                           【点评】本题考查了等比数列的通项公式与求和公式，考查了推理能力与计算能力，属于中档题．                  　                                                                                                                       

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