等比数列中,a3*a4*a5=3 ,a6*a7*a8=24则a9*a10*a11的值等于多少
问题描述：
等比数列中,a3*a4*a5=3 ,a6*a7*a8=24则a9*a10*a11的值等于多少
答
设等比数列的首项a,公比q
a3*a4*a5=3
a6*a7*a8=24=a3q^3*a4q^3*a5q^3=a3*a4*a5*q^9
则q^9=8
a9*a10*a11=a6q^3*a7q^3*a8q^3=a6*a7*a8*q^9=24*8=192
答
设a1=m,a2=km,a3=k^2m,a4=k^3m…an=k^(n-1)m
a3*a4*a5=k^2*k^3*k^4m^3=k^9m^3=3
a6*a7*a8=k^5*k^6*k^7m^3=k^18m^3=24
得:k^9=8;m^3=3/8
则a9*a10*a11=k^8*k^9*k^10m^3=k^27m^3
=(k^9)^3m^3
=8^3*3/8
=3*64
=192