已知{an}为等比数列,a2=2,a5=16,则a1²+a2²+a3²+···+an²=

问题描述:

已知{an}为等比数列,a2=2,a5=16,则a1²+a2²+a3²+···+an²=

a5/a2=q³=8得:q=2,a1=a2/q=1{an}成等比,则{an²}仍成等比,新公比q‘=q²=4所以,a1²+a2²+...+an²=a1²(1-q'^n)/(1-q') =(1-4^n)/(1-4) ...