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{bn}的通向公示；证明：数列bn+1 是等比数列

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$已知等差数列{an}满足a2=3,a5=9,若数列{bn}满足b1=3,bn=a2^n (2^n是a的下标) ,求求{bn}的通向公示；证明：数列bn+1 是等比数列$

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{bn}的通向公示；证明：数列bn+1 是等比数列
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{bn}的通向公示；
证明：数列bn+1 是等比数列

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{bn}的通向公示；证明：数列bn+1 是等比数列
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.

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