问题 解答题
已知等差数列{an}的前n项和为Sn,S5=35,a5和a7的等差中项为13.
(Ⅰ)求an及Sn
(Ⅱ)令bn=
4
a2n
-1
(n∈N),求数列{bn}的前n项和Tn
答案

(Ⅰ) 设等差数列{an}的公差为d,

因为S5=5a3=35,a5+a7=26,

所以

a1+2d=7
2a1+10d=26
,…(2分)

解得a1=3,d=2,…(4分)

所以an=3+2(n-1)=2n+1;

Sn=3n+

n(n-1)
2
×2=n2+2n.…(6分)

(Ⅱ) 由(Ⅰ)知an=2n+1,

所以bn=

4
a2n
-1
=
1
n(n+1)
…(8分)

=

1
n
-
1
n+1
,…(10分)

所以Tn=(1-

1
2
)+(
1
2
-
1
3
)+…+(
1
n
-
1
n+1
)=1-
1
n+1
=
n
n+1
.…(12分)

阅读理解

Riding School:

You can start horse—riding at any age.Choose private or group lessons any weekday

between  9 a.m.and 8:30 P.m.(3:30 p.m.on Saturdays).There are 10 kilometers of tracks and paths for leisurely rides across farmland and open country.You will need a riding hat.

Opening Hours:Monday through Friday:9:00 a.m.—8:30 p.m.

Phone:(412)396—6754  Fax:(412)396—6752

Sailing Club:

Our Young Sailor’s Course leads to the Stage 1 Sailing qualification.You’ll learn how to sail safely and the course also covers sailing theory and first aid.Have fun with other course members , afterwards in the clubroom.There are 10 weekly two-hour 1essons (Tuesdays 6 p.m.~8 p.m.).   

Opening Hours:Tuesdays:6:00 p.m.—8:00 p.m.

Phone:(412)396—6644 Fax:(412)396—6644

Diving Centre: Our experienced instructors offer one-month courses in deep-sea diving for beginners.There are two evening lessons a week,in which you learn to breathe underwater and use the equipment safely.You only need  swimming costume and towel.Reduced rates for couples.

Opening Hours:Monday and Friday:6:30 p.m.—8:30 p.m.

Phone:(412)396—6312  Fax:(412)396—6706

Medical Center:

The staff of the Medical Center aim to provide convenient and comprehensive medical care to students and staff of the university.The center is well equipped and the staff here are trained to deal with a broad range of medical problems.Both female and male doctors as well as nursing staff are available for consultation.Also,all kinds of medicines are sold here and are cheaper for students than other drugstores.

Opening Hours:24 hours from Monday to Sunday

Phone:(412)396--6649  Fax:(412)396—6648

Watersports Club:

We use a two-kilometer length of river for speedboat racing,and water-skiing,A beginners’course consists of ten 20-minute lessons.You will learn to handle boats safely and confidently,but must be able to swim.The club is in a convenient central position and is open daily from 9 a.m to 4 p.m,with lessons all through the day.

Opening Hours:Monday through Friday:9:00 a.m.—4:00 p.m.

Phone: (412)396—6899  Fax396—6890

小题1:If you want to swim and enjoy activities which are fast and a bit dangerous,you should join ________ .

A.Diving Centre

B.Riding School

C.Watersports Club

D.Sailing Club小题2:If you want to experience a new activity in the countryside in the mornings,you may fax _____________________________ .

A.(412)396—6752

B.(412)396—6648

C. (412)396—6876

D.(412)396—6706小题3:If you are planning to explore the ocean depths.you should attend your lessons at ______ .

A.Monday through Friday:7:00 a.m.—10:00 p.m.

B.24 hour from Monday to Sunday

C.Tuesdays:6:00 p.m.—8:00 p.m.

D.Monday and Friday:6:30 p.m.—8:30 p.m.小题4:You want to do an activity one evening a week and get a certificate in the end,you can go to __________________________.

A.Diving Center

B.Sailing Club

C.Riding School

D.Watersports Club小题5:Which is NOT the convenience that the Medical Center provides?

A.Well trained staff members.

B.Nursery for newly-born babies.

C.Good equipment.

D.Various less expensive medicines.

问答题