问题 选择题

已知等比数列{an}满足an>0,n=1,2,…,且a5·a2n5=22n(n≥3),则当n≥1时,log2a1+log2a3+…+log2a2n1=(  )

A.n(2n-1)

B.(n+1)2

C.n2

D.(n-1)2

答案

答案:C

分析:由题意,等比数列{an}a>0,n=1,2,…,且a5?a2n-5=22n(n≥3),又当n>1时,log2a1+log2a3+log2a5+…+log2a2n-1=log2a1a3a5…a2n-1.由等比数列的性质m+n=s+t,aman=asat.求出a1a3a5…a2n-1的值,即可求出正确答案,得出正确选项

解:由题意等比数列{an}a>0,n=1,2,…,

当n>1时,log2a1+log2a3+log2a5+…+log2a2n-1=log2a1a3a5…a2n-1

又a5?a2n-5=22n(n≥3)

∴a1a3a5…a2n-1=(2nn=2n 2

∴log2a1+log2a3+log2a5+…+log2a2n-1=log22n 2=n2

故选C

阅读理解

As nanny(保姆), cook, cleaner, shopper, driver, and gardener, she has one of the most demanding jobs in Britain today. And paying someone else to do the chores(家务活) which take the average housewife 71 hours a week would cost €349.

At over €18,000 a year that’s more than the earnings of 70 percent of the population, including train drivers, firemen, prison officers, and social worker. Looking after a baby less than a year old takes a housewife into a even higher pay league. According to a stud, she earns €457 a week – at nearly €24,000 a year, the same as teachers, engineers, and chemists.

Researchers put a price on each chore, then tried to find out how long the average person takes doing them. They found housewives spend an average 70.7 hours a week on housework – with looking after the children (17.9hours) and cooking and cleaning (12.9 hours each) the most time-consuming(费时).

A wife with a part-time job still works and average of 59 hours a week at home. Those in full-time employment put in longer hours at home than in the workplace. The good news is that these hours sharply as children get older. While the average mother with child under one puts in 90 hours weekly, the figure drops to 80 hours from one to four and to 66 hours from five to ten.

Mother-of-four Karen Williams from London said, “Paying the housewives may not be practical, but the government should recognize the value of housework, perhaps through the tax. Running a house takes a lot of time and most husbands don’t understand this. For example, my husband only puts a shelf up now and again. He never cleans the kitchen – that’s the real test.”

小题1:Who earns most according to the text?

A.A social worker.

B.A fireman.

C.A gardener.

D.A teacher.小题2: We lean from the text that looking after children ______.

A.takes more time than doing any other housework

B.means more duties than being a teacher

C.requires the mother to be well-educated

D.prevents the mother from working outside小题3:According to the text, a housewife with a baby less than one year old may work _____.

A.66 hours a week

B.71 hours a week

C.80 hours a week

D.90 hours a week小题4:By mentioning her husband, Karen Williams wants to show that ______.

A.housework is no easy job

B.her husband has no time to clean the kitchen

C.a housewife needs to be paid for cleaning

D.the kitchen is hard to clean

单项选择题