湖南省益阳市2015-2016学年高二上期末数学试卷(理)含答案解析  
10．以q为公比的等比数列{an}中，a₁＞0，则“a₁＜a₃”是“q＞1”的（　　）                    
A．充分而不必要条件  B．必要而不充分条件                                     
C．充分必要条件         D．既不充分也不必要条件                                    
【分析】根据等比数列的性质，利用充分条件和必要条件的定义进行判断．                  
【解答】解：在等比数列中，若a1＜a3，                                                  
则a₁＜a₁q²，                                                                                       
∵a₁＞0，                                                                                            
∴q₂＞1，即q＞1或q＜﹣1．                                                                   
若q＞1，则a₁q²＞a1，                                                                        
即a₁＜a₃成立，                                                                                  
∴“a₁＜a₃”是“q＞1”成立的必要不充分条件，                                             
故选：B．                                                                                          
【点评】本题主要考查充分条件和必要条件的判断，利用等比数列的通项公式和性质是解决本题的关键．