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问题 解答题

已知：等差数列{an}中，a3+a4=15，a2a5=54，公差d<0.

（I）求数列{an}的通项公式an；

（II）求数列的前n项和Sn的最大值及相应的n的值.

答案

（1）；（2）或11时，取得最大值，最大值为55.

题目分析：（1）根据等差数列的通项公式由a3+a4=15，a2a5=54得一方程组，解这个方程组得公差和首项，从而得数列{an}的通项公式an.

（2）等差数列的前n项和Sn是关于n的二次式，将这个二次式配方即可得最大值.

试题解析：（1）为等差数列，

 解得（因d<0，舍去）

                            6分

（2），

                     9分

又，对称轴为，故当或11时，

取得最大值，最大值为55                   12分

单项选择题

Dear Sirs,
Your shipment of twelve thousand ’Smart’ watches was received by our company this morning. However, we wish to make a number of complaints concerning the serious delay in delivery and your failure to carry out our specific instructions with regard to this order.
It was stressed from the beginning that the delivery date had to be less than six weeks from the initial order in order to meet our own customers’ requirements. While we understand that delays in production are occasionally inevitable, we must point out that the major reason why the order was placed with your company was because we were assured by you of its speed of delivery, and that your existing stocks were sufficiently high to ensure immediate shipment. Late delivery of the goods has caused US to disappoint several of our most valued customers, and is bound to have a negative effect on potential future orders.
The second complaint concerns the difference in color between the watches we ordered and those delivered. It was stated clearly in the original order that watches in combinations of green/purple and orange/purple only were required. However, only half the watches in the delivery received are of the colors specified. Our Hong Kong agent assures US that she stressed to you the importance of following our instructions precisely, since we consider there to be only a limited market in this country for watches of other colors at the present time. Any watches that are not of the specified colors will, of course, be returned to you.
We are also somewhat concerned about the rather poor quality of the goods received, since it is apparent that the watches that finally arrived have been produced from inferior materials and have been manufactured to a lower standard than those in the sample. We have also found that a number of the watches do not appear to be functioning. Whether the latter problem is due to poor manufacture, damage during transportation or bad batteries is not yet clear, but we should like to point out that we feel this matter to be entirely your responsibility.

The manufacturers of "Smart" watches were given the order because ______.
A. they produced the best watches of its kind in the world
B. the watches would be easy to make and the designs were already prepared
C. they promised they could produce enough stocks quite quickly
D. they claimed the order would be easy since the watches were already in stock

As a result of the above problems, therefore, we feel that the most suitable course of action is to return to you unpaid any of the goods considered unsatisfactory, and to subtract any resultant costs from our final settlement. We shall also, of course, be forced to reconsider whether any further orders should be placed with your company.
We look forward to your prompt reply.


Yours sincerely,


John Smith
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单项选择题

企业不再符合相应建筑业企业资质标准要求条件的，其整改期限最长不超过（）个月。

A.1

B.2

C.3

D.5
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