题目

数列，，满足：，，． （1）若数列是等差数列，求证：数列是等差数列； （2）若数列，都是等差数列，求证：数列从第二项起为等差数列； （3）若数列是等差数列，试判断当时，数列是否成等差数列？证明你的结论． 答案：证明：（１）设数列的公差为， ∵， ∴， ∴数列是公差为的等差数列．        ………………４分 （２）当时，， ∵，∴，∴， ∴， ∵数列，都是等差数列，∴为常数， ∴数列从第二项起为等差数列．       ………………１０分 （３）数列成等差数列．解法１ 设数列的公差为， ∵， ∴，∴阅读下面的短文，将划线部分的句子译成汉语。     1 Dreams may be more important than sleep. Some people don't need very much sleep. But we all need to dream, scientists say.      2 Dreams take up about one quarter of our sleeping time. People have several dreams each night. Dreams are like short movies. They are usually in color. Some dreams are like old movies. They come to us over and over again. That may be because the dreamer is worrying about something. 3 Dreaming may be a way of trying to find an answer.      Some people get new ideas about their work from dreams. They could have been thinking about their work all day. These thoughts can carry over into dreams.      Sometimes we wake up with a good feeling from a dream. But often we can't remember the dream. Dreams can disappear quickly from memory.     Too much dreaming can be harmful. The more we sleep, the longer we dream. 4 The mind is hard at work when we dream. 5 That is why we may have a long sleep and still wake up tired. 1____________________________________________2____________________________________________3____________________________________________4____________________________________________5____________________________________________