Question

已知等差数列{an}满足a2=3,a5=9,若数列{bn}满足b1=3,bn=a2^n (2^n是a的下标) ,求求{b

Answer 1

题目错了,应该是数列{bn -1}是等比数列,那个+号应该是-号.

证：

设{an}公差为d

a5-a2=3d=9-3=6

d=2

a1=a2-d=3-2=1

an=a1+(n-1)d=1+2(n-1)=2n+1

bn=a(2^n)=2×2^n +1=2^(n+1) +1

数列{bn}的通项公式为bn=2^(n+1) +1

bn-1=2^(n+1) +1-1=2^(n+1)

b1=a(2^1)=a2=3

b1-1=3-1=2

[b(n+1) -1]/(bn -1)=2^(n+2)/2^(n+1)=2,为定值.

数列{bn -1}是以2为首项,2为公比的等比数列.