问题 解答题

已知等差数列{an}的前n项和胃Sn,公差d≠0,且S3+S5=50,a1,a4,a13成等比数列.

(1)求数列{an}的通项公式;

(2)若从数列{an}中依次取出第2项、第4项、第8项,…,第2n项,…,按原来顺序组成一个新数列{bn},记该数列的前n项和为Tn,求Tn的表达式.

答案

(1)设等差数列的公差为d,则

∵S3+S5=50,a1,a4,a13成等比数列,

∴3a1+3d+5a1+10d=50,(a1+3d)2=a1(a1+12d)

∵公差d≠0,∴a1=3,d=2

∴数列{an}的通项公式an=2n+1;

(2)据题意得bn=a2n=2×2n+1.

∴数列{bn}的前n项和公式:Tn=(2×2+1)+(2×22+1)+…+(2×2n+1)=2×(2+22+…+2n)+n=2×

2(1-2n)
1-2
+n=2n+2+n-4.

单项选择题 A型题
阅读理解

Most recently, it’s very common in students who need a parent present for job interviews.

Naturally, it’s easy to blame the students in these situations, but the bigger problem is us. We—as parents—are so eager to protect our kids that we fail to realize that this in itself is harming them. As the mother of two young sons, I have to remind myself all the time that the biggest responsibility I have as a parent is to help them develop the skills needed to live in, to live without me. So, I’ll let them fail.

I’ll let them fail because as long as they are safe and warm inside their comfort zones, they will never grow. And failure—along with loss, heartbreak, disappointment, etc.—will be part of growth for them. Call me the anti-tiger mom, but leaving them alone is my way of helping them become equipped to fit in this world as we know it today. From terrorism (恐怖主义) and seemingly endless natural disasters, to our national debt and beyond, if we expect the next generation to stand up to the very real problems of our time, we need to stop feeding them and start teaching them how to fish.

My children are faced with hard situations in their own life almost each day, but they try to negotiate (协商) everything now. It’s a small price to help them learn a skill they’ll use for the rest of their lives, including when I don’t come with them on job interviews. 

小题1:Why do parents go along with their kids on job interviews?

A.Because they want to protect their kids from difficulties.

B.Because they think they can protect them from being hurt.

C.Because their kids are too shy to attend interviews.

D.Because their kids strongly request them to do so.小题2:According to the author, what is helpful to kids’ development?

A.Protecting them.

B.Keeping them safe.

C.Leaving them alone.

D.Blaming them.小题3:The author believes experiencing failure in life can make kids ___________.

A.become healthier than other kids

B.grow in this challenging world

C.develop all social skills

D.escape from natural disasters小题4:If the writer’s boy goes to a job interview, she probably will ___________.

A.go with him to protect her kid from difficulty

B.stay home but give him directions over telephone

C.wait outside and talk with other parents

D.let him go to the interview by himself小题5:Which of the following might be the best title of the text?

A.Never help your kids

B.Let your kids fail

C.Go to the interview with your kids

D.Live without parents