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问题 选择题
在数列{an}中，对于任意的正整数n都有a1+a2+…+an=3n-1，则{an2}的前n项和为（　　）
A．9n-1B．
9n-1
2
C．
9n-1
4
D．
4
9
答案

∵a1+a2+a3+…+an=3n-1，①

∴a1+a2+a3+…+an+1=3n+1-1，②

②-①得：an+1=3n+1-3n=2×3n，

∴an=2×3n-1．

当n=1时，a1=31-1=2，符合上式，

∴an=2×3n-1．

∴an2=4×9n-1，∴a12=4，

∴{an2}是以4为首项，9为公比的等比数列，

∴a12+a22+a32+…+an2=

4(1-9n)
1-9
=
9n-1
2
，

故选B．

单项选择题

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A. Request assistance from the neonatal resuscitation team.
B. Place the client on bed rest on her left side.
C. Obtain equipment for an amniotomy.
D. Prepare terbutaline in an intravenous solution of normal salin
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