已知数列{log2(a^n-1}为等差数列,且a1=3,a2=5.1.求证：数列{an-1}是等比数列.

题目

已知数列{log2(a^n-1}为等差数列,且a1=3,a2=5.1.求证：数列{an-1}是等比数列.

答案

解: 由{log2(a^n-1)}为等差数列 则设公差为d 则有: d=log2(a2-1)-log2(a1-1) =2-1 =1 则有: log2(an-1)=log2(a1-1)+(n-1)d =1+(n-1) =n ...