问题
选择题
数列{an}满足3+an=an+1(n∈N+)且a2+a4+a6=9,则log
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答案
∵3+an=an+1
∴an+1-an=3
∴数列{an}是以3为公差的等差数列
由等差数列的性质可得,a2+a4+a6=3a4=9
∴a4=3,a7=a4+3d=12
∴log
(a5+a7+a9)=log1 6
3a7=log1 6
36=-21 6
故选A
数列{an}满足3+an=an+1(n∈N+)且a2+a4+a6=9,则log
|
∵3+an=an+1
∴an+1-an=3
∴数列{an}是以3为公差的等差数列
由等差数列的性质可得,a2+a4+a6=3a4=9
∴a4=3,a7=a4+3d=12
∴log
(a5+a7+a9)=log1 6
3a7=log1 6
36=-21 6
故选A