问题 解答题

有一组数据:x1,x2,…,xn(x1<x2<…<xn)的算术平均值为10,若去掉其中最大的一个,余下数据的算术平均值为9;若去掉其中最小的一个,余下数据的算术平均值为11.   

(1)求出第一个数x1关于n的表达式及第n个数xn关于n的表达式.

(2)若x1,x2,…,xn都是正整数,试求第n个数xn的最大值,并举出满足题目要求且xn取到最大值的一组数据.

答案

(1)依条件得:

x1+x2+…+xn=10n         (1)
x1+x2+…+xn-1=9(n-1)  (2)
x2+x3+…+xn=11(n-1)     (3)   

由(1)-(2)得:xn=n+9,

又由(1)-(3)

得x1=11-n

(2)由于x1是正整数,故 x1=11-n≥1,

⇒1≤n≤10,故xn=n+9≤19

当n=10时,x1=1,x10=19,x2+x3+…+x9=80,

此时,x2=6,x3=7,x4=8,x5=9,x6=11,x7=12,x8=13,x9=14.

阅读理解

判断  阅读下面的材料,判断下列句子是否符合短文内容。符合内容的写(T)不符合的写(F)。(T="True," F= False)

Last Friday after I got my pay, I went shopping on my way home. In the crowded supermarket, I lost my purse and my money was gone with it. I felt very angry and sad. We were not rich and the money was important for us. How could I tell my wife about it?

I felt really sorry for losing the money. When I got home, I cleaned the house and prepared a nice meal. I hoped what I did could comfort(安慰) my wife. When she came back, she was surprised to see the clean house and the nice meal. Then I began to tell my story when we were at table, but my wife didn't respond (反映) as if she had not heard my words. Maybe she was trying hard to hide her anger, I thought.

“I've lost my pay." I said to her again.

“I see.” She didn't seem to be angry with me. For a moment, she said nothing but enjoyed the meal with me.

“I've lost my money," I could not help asking, “why don't you blame (责备) me?"

“Oh, my dear," she raised her eyes, looked at me and said, "I'm thinking about how to comfort you. It's the thief who is to be blamed!"

根据短文内容,判断句子正误,正确的写“T”,错误的写“F”

小题1:I got my pay last Monday.

小题2:In the supermarket I lost my purse and money.

小题3:I cleaned the house because I liked doing it.

小题4:My wife was surprised to see what I did.

小题5:When my wife heard my story, she became very angry.

单项选择题