正项的等差数列{an}中,2a3-a72+2a11=0,数列{bn}是等比数列,且b7=a7,则b6b8=_.

问题描述:

正项的等差数列{an}中,2a3-a72+2a11=0,数列{bn}是等比数列,且b7=a7,则b6b8=______.

根据等差数列的性质得:a3+a11=2a7
2a3-a72+2a11=0变为:4a7-a72=0,解得a7=4,a7=0(舍去),
所以b7=a7=4,
则b6b8=a72=16.
故答案为:16