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问题 解答题
已知{an}是各项均为正数的等比数列，且a1+a2=2(
1
a1
+
1
a2
)，a3+a4=32(
1
a3
+
1
a4
)．
（Ⅰ）求{an}的通项公式；
（Ⅱ）设bn=an2+log2an，求数列{bn}的前n项和Tn．
答案

（Ⅰ）设等比数列{an}的公比为q，则an=a1qn-1，由已知得：

a1+a1q=2(
1
a1
+
1
a1q
) 
a1q2+a1q3 =32(
1
a1q2
+
1
a1q3
) 
，

化简得：

a12q(q+1)=2(q+1)
a12q5 (q+1)=32(q+1)
，即
a12q=2
a12q5=32
，

又a1＞0，q＞0，解得：

a1=1
q=2
，

∴an=2n-1；

（Ⅱ）由（Ⅰ）知bn=an2+log2an=4n-1+（n-1）

∴Tn=（1+4+42+…+4n-1）+（1+2+3+…+n-1）

=

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

=

4n-1
3
+
n(n-1)
2
．

改错题

短文改错（每小题1分，满分10分）

文章共有10处语言错误，要求你在错误的地方增加、删除或修改某个单词。

增加：在缺词处加一个漏字符号（∧），并在其下面写上该加的词。

删除：把多余的词用斜线（\）划掉。

修改：在错的词下划一横线，并在该词下面写上修改后的词。

注意：1．每处错误及修改词均仅限一词；

2．只允许修改10处，多者（从11处起）不记分。

As an English beginner, I found difficult to read fast. It was because whenever I read I always try to translate every English word or sentence into Chinese after I could understand it. As a result of, it usually took me over 10 minutes to finish read a passage. To get it over, I read a lot. Firstly, you read the passage fast and answered the questions within six minutes. Secondly, I checked the answer to see which of them were wrong. Then I look up only those key new words to seeing why they were wrong. By this way, I have improved my reading speed a lot.

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选择题

有X、Y、Z三种金属，把X和Y放入稀HCl中，X溶解Y不溶解；把Y和Z分别放入AgNO3溶液中，Y表面有银析出而Z没有变化，则X、Y、Z的金属活动顺序是（　　）

A．X＞Y＞Z

B．X＞Z＞Y

C．Z＞Y＞X

D．Z＞X＞Y
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