已知数列{an}满足a1=1 ,an+1=3an+2的n+1次幂,求an

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已知数列{an}满足a1=1,an+1=3an+2的n+1次幂,求an已知数列{an}满足a1=1,an+1=3an+2的n+1次幂,求an已知数列{an}满足a1=1,an+1=3an+2的n+1次

已知数列{an}满足a1=1 ,an+1=3an+2的n+1次幂,求an
已知数列{an}满足a1=1 ,an+1=3an+2的n+1次幂,求an

已知数列{an}满足a1=1 ,an+1=3an+2的n+1次幂,求an
a(n+1)=3an+2^(n+1)
设a(n+1)+k*2^(n+1)=3[a(n)+k*2^n]
则 a(n+1)=3an+3k*2^n-2k*2^n=3an+k*2^n
所以 k=2
即 a(n+1)+2*2^(n+1)=3[a(n)+2*2^n]
所以 {an+2*2^n}是等比数列
首项为a1+2*2^1=5,公比为3
所以 an+2*2^n=5*3^(n-1)
an=5*3^(n-1)-2^(n+1)

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