等比数列{an}中,a1+a2+a3=30,a4+a5+a6==60,求a10+a11+a12.

题目

等比数列{an}中,a1+a2+a3=30,a4+a5+a6==60,求a10+a11+a12.
等比数列｛an｝中,a1+a2+a3=30,a4+a5+a6==60,求a10+a11+a12.

答案

a1+a2+a3=30
a4+a5+a6=60
即a1*q^3+a2*q^3+a3*q^3=60
q^3(a1+a2+a3)=60
q^3=60/30=2
a10+a11+a12
=a4*q^6+a5*q^6+a6*q^6
=q^6(a4+a5+a6)
=4*60
=240