题目内容
设{an}为等差数列,{bn}为等比数列,a1=b1=1,a2+a4=b3,b2·b4=a3,分别求出{an}及{bn}的前n项和S10及T10.
S10=10a1+
d=-![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637054254.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231236371011818.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637039316.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637054254.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231236371011818.gif)
∵{an}为等差数列,{bn}为等比数列,∴a2+a4=2a3,b2·b4=b32,
已知a2+a4=b3,b2·b4=a3,∴b3=2a3,a3=b32,
得b3=2b32,∵b3≠0,∴b3=
,a3=
.
由a1=1,a3=
,知{an}的公差d=-
,
∴S10=10a1+
d=-
.
由b1=1,b3=
,知{bn}的公比q=
或q=-
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231236371011818.gif)
已知a2+a4=b3,b2·b4=a3,∴b3=2a3,a3=b32,
得b3=2b32,∵b3≠0,∴b3=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637117213.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637132220.gif)
由a1=1,a3=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637132220.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637163228.gif)
∴S10=10a1+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637039316.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637054254.gif)
由b1=1,b3=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637117213.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637226259.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823123637226259.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231236371011818.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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