问题 解答题
等比数列{an}中,a1,a2,a3分别是下表第一、二、三行中的某一个数,且a1,a2,a3中的任何两个数不在下表的同一列.
 
第一列
第二列
第三列
第一行
3
2
10
第二行
6
4
14
第三行
9
8
18
 
(1)求数列{an}的通项公式;
(2)若数列{bn}满足:bn=an+(-1)nlnan,求数列{bn}的前2n项和S2n.
答案

(1) an=2·3n-1     (2)S2n=32n+nln3-1

解:(1)当a1=3时,不合题意;

当a1=2时,当且仅当a2=6,a3=18时,符合题意;

当a1=10时,不合题意.

因此a1=2,a2=6,a3=18,所以公比q=3.

故an=2·3n-1.

(2)因为bn=an+(-1)nlnan,

=2×3n-1+(-1)nln(2×3n-1)

=2×3n-1+(-1)n[ln2+(n-1)ln3]

=2×3n-1+(-1)n(ln2-ln3)+(-1)nnln3.

所以S2n=b1+b2+…+b2n=2(1+3+…+32n-1)+[-1+1-1+…+(-1)2n](ln2-ln3)+[-1+2-3+…+(-1)2n2n]ln3=2×+nln3=32n+nln3-1.

多项选择题
阅读理解

A nine-year-old kid was sitting at his desk when suddenly there was a puddle(水潭、泥坑) between his feet and the front of his trousers was wet.He thought his heart was going to stop because he couldn't possibly imagine how this had happened.It had never happened before, and he knew that when the boys found out he would never hear the end of it. When the girls found out, they would never speak to him again as long as he lived.

He prayed this prayer, "Dear God, I need help  now! Five minutes from now I'm dead meat!" He looked up from his prayer and here came the teacher with a look in her eyes that said he had been discovered.As the teacher was walking toward him, a classmate named Susie was carrying a goldfish bowl full of water.Susie tripped (绊倒) in front of the teacher and dumped (倒) the bowl of water in the boy's lap.The boy pretended to be angry, but all the while was saying to himself, "Thank you.Lord!"

Now all of a sudden, instead of being the object of ridicule, the boy was the object of sympathy.The teacher rushed him downstairs and gave him gym shorts to put on while his trousers dried out.All the other children were on their hands and knees cleaning up around his desk.The sympathy was wonderful.But as life would have it, the ridicule that should have been his had been transferred (转移) to someone else+—Susie.She tried to help, but they told her to get out.

When school was over, the boy walked over to Susie and whispered, "You did that on purpose, didn't you?" Susie whispered back, "I wet my trousers once, too!"

小题1:The underlined sentence in Paragraph 1 means ____       .

A.the boys would never play with him

B.the boys would treat him as usual

C, he would hardly hear any praise from the boys

D.he would be laughed at by the.boys endlessly

小题2:After Susie dumped water in his lap, the boy was in a state of ___      _.

A.excitement

B.relief

C.anxiety

D.anger小题3:What did the other kids do after the incident?

A.They offered him dry clothes.

B.They laughed at the boy rudely,

C.They helped the boy do the cleaning.

D.They urged the boy to get out angrily,小题4:Why did Susie dump water in the boy's lap?

A.The boy asked her to do so.

B.She just did it by accident.

C.The teacher tripped her on purpose.

D.She knew the boy's embarrassment.