在数列{an}中,a1=2,an+1=3an+2.(其中n+1为下标)a(n+1)=3an+2a(n+1)+1=3an+3a(n+1)+1=3(an +1)[a(n+1)+1]/(an +1)=3,为定值.a1+1=2+1=3数列{an +1}是以3为首项,3为公比的等比数列.(注意)an +1=3^nan=3^n-1n=1时,a1=3-1=2,同样满足
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![在数列{an}中,a1=2,an+1=3an+2.(其中n+1为下标)a(n+1)=3an+2a(n+1)+1=3an+3a(n+1)+1=3(an +1)[a(n+1)+1]/(an +1)=3,为定值.a1+1=2+1=3数列{an +1}是以3为首项,3为公比的等比数列.(注意)an +1=3^nan=3^n-1n=1时,a1=3-1=2,同样满足](/uploads/image/z/6755536-64-6.jpg?t=%E5%9C%A8%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Ca1%3D2%2Can%2B1%3D3an%2B2.%28%E5%85%B6%E4%B8%ADn%2B1%E4%B8%BA%E4%B8%8B%E6%A0%87%29a%28n%2B1%29%3D3an%2B2a%28n%2B1%29%2B1%3D3an%2B3a%28n%2B1%29%2B1%3D3%28an+%2B1%29%5Ba%28n%2B1%29%2B1%5D%2F%28an+%2B1%29%3D3%2C%E4%B8%BA%E5%AE%9A%E5%80%BC.a1%2B1%3D2%2B1%3D3%E6%95%B0%E5%88%97%7Ban+%2B1%7D%E6%98%AF%E4%BB%A53%E4%B8%BA%E9%A6%96%E9%A1%B9%2C3%E4%B8%BA%E5%85%AC%E6%AF%94%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97.%EF%BC%88%E6%B3%A8%E6%84%8F%EF%BC%89an+%2B1%3D3%5Enan%3D3%5En-1n%3D1%E6%97%B6%2Ca1%3D3-1%3D2%2C%E5%90%8C%E6%A0%B7%E6%BB%A1%E8%B6%B3)
在数列{an}中,a1=2,an+1=3an+2.(其中n+1为下标)a(n+1)=3an+2a(n+1)+1=3an+3a(n+1)+1=3(an +1)[a(n+1)+1]/(an +1)=3,为定值.a1+1=2+1=3数列{an +1}是以3为首项,3为公比的等比数列.(注意)an +1=3^nan=3^n-1n=1时,a1=3-1=2,同样满足
在数列{an}中,a1=2,an+1=3an+2.(其中n+1为下标)
a(n+1)=3an+2
a(n+1)+1=3an+3
a(n+1)+1=3(an +1)
[a(n+1)+1]/(an +1)=3,为定值.
a1+1=2+1=3
数列{an +1}是以3为首项,3为公比的等比数列.(注意)
an +1=3^n
an=3^n-1
n=1时,a1=3-1=2,同样满足.
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但是“注意”那步中,我认为应该是数列a(n+1)+1是以3为首项,3为公比的等比数列
所以a(n+1)=3^n-1
所以我求出的是3n^(n-1)+1
请问为什么
在数列{an}中,a1=2,an+1=3an+2.(其中n+1为下标)a(n+1)=3an+2a(n+1)+1=3an+3a(n+1)+1=3(an +1)[a(n+1)+1]/(an +1)=3,为定值.a1+1=2+1=3数列{an +1}是以3为首项,3为公比的等比数列.(注意)an +1=3^nan=3^n-1n=1时,a1=3-1=2,同样满足
令bn=(an )+1,则bn是以3为首项,3为公比的等比数列,当然,b(n+1)也是以3为首项,3为公比的等比数列.所以b(n+1)=b1*3^n=3^(n+1),
即a(n+1)+1=3^(n+1)