已知等比数列an的通项公式an=3*(0.5)^(n-1)且bn=a3n-2+a3n-1+a3n求证bn成等比数列

题目

已知等比数列an的通项公式an=3*(0.5)^(n-1)且bn=a3n-2+a3n-1+a3n求证bn成等比数列

答案

{an}为等比数列,
则an+1=an*q,n>=1
bn+1/bn=(a3n+1+a3n+2+a3n+3)/(a3n-2+a3n-1+a3n)
=(q^3*a3n-2+q^3*a3n-1+q^3*a3n)/(a3n-2+a3n-1+a3n)
=q^3
上式对任意正整数n成立
则{bn}为等比数列