設(shè){an}是公比為q的等比數(shù)列,|q|>1,令bn=an+1(n=1,2,…),若數(shù)列{bn}有連續(xù)四項在集合{-53,-23,19,37,82}中,則6q= .
【答案】
分析:根據(jù)B
n=A
n+1可知 A
n=B
n-1,依據(jù){Bn}有連續(xù)四項在{-53,-23,19,37,82}中,則可推知則{A
n}有連續(xù)四項在{-54,-24,18,36,81}中,按絕對值的順序排列上述數(shù)值,相鄰相鄰兩項相除發(fā)現(xiàn)-24,36,-54,81是{A
n}中連續(xù)的四項,求得q,進而求得6q.
解答:解:{Bn}有連續(xù)四項在{-53,-23,19,37,82}中
B
n=A
n+1 A
n=B
n-1
則{A
n}有連續(xù)四項在{-54,-24,18,36,81}中
{A
n}是等比數(shù)列,等比數(shù)列中有負(fù)數(shù)項則q<0,且負(fù)數(shù)項為相隔兩項
等比數(shù)列各項的絕對值遞增或遞減,按絕對值的順序排列上述數(shù)值
18,-24,36,-54,81
相鄰兩項相除
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/0.png)
=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/1.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/2.png)
=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/3.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/4.png)
=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/5.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/6.png)
=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/7.png)
很明顯,-24,36,-54,81是{A
n}中連續(xù)的四項
q=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/8.png)
或 q=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/9.png)
(|q|>1,∴此種情況應(yīng)舍)
∴q=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024181210379972412/SYS201310241812103799724011_DA/10.png)
∴6q=-9
故答案為:-9
點評:本題主要考查了等比數(shù)列的性質(zhì).屬基礎(chǔ)題.