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问题 解答题

已知数列{xn}的首项x1=3，通项xn=2np+np（n∈N*，p，q为常数），且成等差数列．求：

（Ⅰ）p，q的值；

（Ⅱ）数列{xn}前n项和Sn的公式．

答案

（Ⅰ）∵x1=3，

∴2p+q=3，①

又x4=24p+4q，x5=25p+5q，且x1+x3=2x4，

∴3+25p+5q=25p+8q，②

联立①②求得 p=1，q=1

（Ⅱ）由（1）可知xn=2n+n

∴Sn=（2+22+…+2n）+（1+2+…+n）

=2n+1-2+

n(n+1)
2
．

改错题

My favourite sport is football. I was a member of      76. ________

our school football team. We practise for three times   77. ________

every week and often watch football match on TV     78. ________

together. Play football not only makes us grow up     79. ________

tall and strong but also give us a sense of fair play     80. ________

and team spirit. We must keep in mind that we play    81. ________

for the team instead ourselves. Also, the sport teaches  82. ________

us the important of obedience. Each player must      83. ________

obey captain, who is the leader of the team.          84. ________

And they must not break the rules too often if we      85. ________

want to win the game.

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解答题
先化简，再求代数式的值：(
2
a+1
+
a+2
a2-1
)÷
a
a-1
，其中a=tan60°-2sin30°．
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