问题 解答题

设等比数列{an}的前n项和为Sna4a1-9,a5a3a4成等差数列.

(1)求数列{an} 的通项公式;

(2)证明:对任意k∈N*Sk+2SkSk+1成等差数列.

答案

(1)an=(-2)n-1n∈N*(2)见解析

(1)解:在等比数列{an}中,a5a3a4成等差数列,

∴2a3a5a4

即2a1q2a1q4a1q3,整理得:q2q-2=0.

解得q=1,或q=-2.

a4a1-9,即a1q3a1-9,

q=1时,无解.

q=-2时,解得a1=1

∴等比数列{an}通项公式为an=(-2)n-1n∈N*

(2)证明:∵Sn为等比数列{an}的前n项和,

SkSk+1Sk+2

Sk+1Sk+2=2·=2Sk.

Sk+1SkSk+2成等差数列.

阅读理解

阅读理解。

     John sent for a doctor because his wife was ill. He called the doctor and made sure they would meet

at five. He arrived at the doctor's at twenty to five. He thought," It's a little bit earlier. I'll wait for a

moment. It's good to keep the time."

    Then he stopped his car in front of the doctor's. He looked around and saw a noisy square (厂场)

not far from here. He went there and sat down on a chair to enjoy the last light of afternoon sun and

make himself quiet. He saw some children playing and some women talking to each other happily.

    Suddenly he heard a girl crying. He came up to her and asked some questions. Then he knew she

got lost. John tried to find out her address and took her home. The girl's parents were very thankful.

    Then John hurried to the doctor's. The doctor said angrily when he saw him, "You're late. Why did

you keep me waiting for twenty minutes?" John said nothing but one word "Sorry! "

l. John drove to the doctor's _____.  

A. late            

B. on time

C. in time          

D. in no time

2. John went to the square to _____.

A. spend the time

B. enjoy himself

C. see the children and the women

D. help the girl

3. The girl cried because _____. 

A. someone hit her

B. she fell off her bike

C. her parents were angry with her

D. she didn't find the way home

4. At last John got to the doctor's at _____.  

A. twenty to five

B. twenty past five

C. five o'clock

D. forty past five

5. From the story, we know John is a _____.

A. busy person    

B. quiet person

C. helpful person    

D. lucky person  

单项选择题