Sn是数列{an}的前n项和，则“Sn是关于n的二次函数”是“数列{an}为等差数列”的( )
A．充分不必要条件
B．必要不充分条件
C．充分必要条件
D．既不充分也不必要条件
答案：D
若Sn是关于n的二次函数，则设为Sn＝an2＋bn＋c(a≠0)，则当n≥2时，有an＝Sn－Sn－1＝2an＋b－a，当n＝1时，S1＝a＋b＋c，只有当c＝0时，数列{an}才是等差数列；若数列{an}为等差数列，则Sn＝na1＋
n，当d≠0时为二次函数，当d＝0时，为一次函数，所以“Sn是关于n的二次函数”是“数列{an}为等差数列”的既不充分也不必要条件．
Many students have hobbies, such as reading, painting, growing vegetables in their gardens, and looking after animals. Some hobbies are relaxing and ___(46) are creative. Hobbies can develop your interests and help you learn new skills. David Smith is a student. His hobby is writing. ___(47) the summer of 2000, he spent four weeks on a summer camp. As well as the usual activities, such as sailing, climbing and mounting biking, there was a writing workshop with a profession ___(48). “She asked us to imagine that we were in a story. Then we wrote about our ___(49) at the camp.” In senior high school David wrote a story about teenage life, and it ___(50) as a book in 2003. Many teenagers love his book, and as a result, David has become a ___(51) young writer. David has been very lucky ___(52) his hobby has brought him enjoyment and success. But he is ___(53) interested in many other things. “I like playing volleyball, too.” says David. “I spend some of my free time playing volleyball for my school team. ___(54) I’ll write more books in the future, but I’m not sure.” It’s something difficult ___(55) that we shouldn’t spend all our time on our favourite hobby. There are many other interesting things to do in life, and we should try to do something new or different.
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