数列{an}是公比为1/2的等比数列,已知a1+a4+a7+.+a97=100求a3+a6+a9+.+a99的值
问题描述：
数列{an}是公比为1/2的等比数列,已知a1+a4+a7+.+a97=100求a3+a6+a9+.+a99的值
答
a(n)=b/2^(n-1)
a(3n-2)=b/2^(3n-3)=b/8^(n-1)
a(3n)=b/2^(3n-1)=(1/4)*b/2^(3n-3)=(1/4)a(3n-2)
100=a(3*1-2)+a(3*2-2)+...+a(3*33-2)
a(3*1)+a(3*2)+...+a(3*33)=(1/4)[a(3*1-2)+a(3*2-2)+...+a(3*33-2)]=(1/4)*100=25