已知数列{An}满足A(n+1)*2=An*2+4,且A1=1,An>0,求An通项公式?令Bn=An*2(n?N)则:Bn+1=Bn+4即:Bn+1-Bn=4又因为B1=A1*2=1 所以Bn=1+(n-1) *4=4n-3即:An=(4n-3)开根号(n?N)
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![已知数列{An}满足A(n+1)*2=An*2+4,且A1=1,An>0,求An通项公式?令Bn=An*2(n?N)则:Bn+1=Bn+4即:Bn+1-Bn=4又因为B1=A1*2=1 所以Bn=1+(n-1) *4=4n-3即:An=(4n-3)开根号(n?N)](/uploads/image/z/14360485-13-5.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3A%28n%2B1%29%2A2%3DAn%2A2%2B4%2C%E4%B8%94A1%3D1%2CAn%3E0%2C%E6%B1%82An%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%3F%E4%BB%A4Bn%3DAn%2A2%28n%3FN%29%E5%88%99%EF%BC%9ABn%2B1%3DBn%2B4%E5%8D%B3%EF%BC%9ABn%2B1-Bn%3D4%E5%8F%88%E5%9B%A0%E4%B8%BAB1%3DA1%2A2%3D1+%E6%89%80%E4%BB%A5Bn%3D1%2B%28n-1%29+%2A4%3D4n-3%E5%8D%B3%EF%BC%9AAn%3D%284n-3%29%E5%BC%80%E6%A0%B9%E5%8F%B7%28n%3FN%29)
已知数列{An}满足A(n+1)*2=An*2+4,且A1=1,An>0,求An通项公式?令Bn=An*2(n?N)则:Bn+1=Bn+4即:Bn+1-Bn=4又因为B1=A1*2=1 所以Bn=1+(n-1) *4=4n-3即:An=(4n-3)开根号(n?N)
已知数列{An}满足A(n+1)*2=An*2+4,且A1=1,An>0,求An通项公式?
令Bn=An*2(n?N)
则:Bn+1=Bn+4
即:Bn+1-Bn=4
又因为
B1=A1*2=1
所以Bn=1+(n-1) *4
=4n-3
即:An=(4n-3)开根号(n?N)
已知数列{An}满足A(n+1)*2=An*2+4,且A1=1,An>0,求An通项公式?令Bn=An*2(n?N)则:Bn+1=Bn+4即:Bn+1-Bn=4又因为B1=A1*2=1 所以Bn=1+(n-1) *4=4n-3即:An=(4n-3)开根号(n?N)
A(n+1)^2=An^2+4
A(n+1)^2-An^2=4
∴An^2是首项为A1^2=1,公差为4的等差数列.
An^2=1+4(n-1)=4n-3
An=(4n-3)开根号
A(n+1)^2是A(n+1)的平方
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