已知数{An}满足An+1=3An+3ˆ(n+1)-1(n∈N+),且A4=365,求数列{An}通项An如题,脚码打不出来,
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![已知数{An}满足An+1=3An+3ˆ(n+1)-1(n∈N+),且A4=365,求数列{An}通项An如题,脚码打不出来,](/uploads/image/z/6133002-42-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%7BAn%7D%E6%BB%A1%E8%B6%B3An%2B1%3D3An%2B3%26%23710%3B%EF%BC%88n%2B1%EF%BC%89-1%28n%E2%88%88N%2B%29%2C%E4%B8%94A4%3D365%2C%E6%B1%82%E6%95%B0%E5%88%97%7BAn%7D%E9%80%9A%E9%A1%B9An%E5%A6%82%E9%A2%98%2C%E8%84%9A%E7%A0%81%E6%89%93%E4%B8%8D%E5%87%BA%E6%9D%A5%2C)
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已知数{An}满足An+1=3An+3ˆ(n+1)-1(n∈N+),且A4=365,求数列{An}通项An如题,脚码打不出来,
已知数{An}满足An+1=3An+3ˆ(n+1)-1(n∈N+),且A4=365,求数列{An}通项An
如题,脚码打不出来,
已知数{An}满足An+1=3An+3ˆ(n+1)-1(n∈N+),且A4=365,求数列{An}通项An如题,脚码打不出来,
A(n+1)=3An+3*(n+1)-1 ======>>>
==>>>> A(n+1)-(1/2)×3^(n+2)-(1/2)=3An-(3/2)×3^(n+1)-(3/2)
==>>>> A(n+1)-(1/2)×3^(n+2)-(1/2)=3[An-(1/2)×3^(n+1)-(1/2)]
===>>>> [A(n+1)-(1/2)×3^(n+2)-(1/2)]/[An-(1/2)×3*(n+1)-(1/2)]=3=常数
则数列{An-(1/2)×3^(n+1)-(1/2)}是以A1-(1/2)×3²-(1/2)为首项、以q=3为公比的等比数列.这个等比数列的第四项是A4-(1/2)×3^5-(1/2)=243=243=3^5
An-(1/2)×3^(n+1)-(1/2)=[3^5]×3^(n-4)=3^(n+1)
An=(1/2)×[3^(n+2)+1]
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已知数{An}满足An+1=3An+3ˆ(n+1)-1(n∈N+),且A4=365,求数列{An}通项An如题,脚码打不出来,
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