问题
选择题
正项等比数列{an}中,a1a5+2a3a6+a1a11=16,则a3+a6的值为( )
A.3
B.4
C.5
D.6
答案
根据等比中项的性质可知a1a5=a23,a1a11=a26,
∴a1a5+2a3a6+a1a11=a23+2a3a6+a26=(a3+a6)2=16
∵a3+a6>0
∴a3+a6=4
故选B
正项等比数列{an}中,a1a5+2a3a6+a1a11=16,则a3+a6的值为( )
A.3
B.4
C.5
D.6
根据等比中项的性质可知a1a5=a23,a1a11=a26,
∴a1a5+2a3a6+a1a11=a23+2a3a6+a26=(a3+a6)2=16
∵a3+a6>0
∴a3+a6=4
故选B