设数列{an}的前n和为Sn,己知a1=1,Sn+1=4an+2,则{an}的通项公式为an=______.
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![设数列{an}的前n和为Sn,己知a1=1,Sn+1=4an+2,则{an}的通项公式为an=______.](/uploads/image/z/362684-20-4.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E5%92%8C%E4%B8%BASn%2C%E5%B7%B1%E7%9F%A5a1%3D1%2CSn%2B1%3D4an%2B2%2C%E5%88%99%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E4%B8%BAan%3D______.)
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设数列{an}的前n和为Sn,己知a1=1,Sn+1=4an+2,则{an}的通项公式为an=______.
设数列{an}的前n和为Sn,己知a1=1,Sn+1=4an+2,则{an}的通项公式为an=______.
设数列{an}的前n和为Sn,己知a1=1,Sn+1=4an+2,则{an}的通项公式为an=______.
A1+A2=S2=4A1+2
A2=3A1+2=5
S(n+1)=4An+2
Sn=4A(n-1)+2
A(n+1)=S(n+1)-Sn=4An-4A(n-1)
A(n+1)-2An=2An-4A(n-1)=2(An-2A(n-1))
A2-2A1=5-2=3
{A(n+1)-2An}是以3为首项,2为公比的等比数列
A(n+1)-2An=3×2^(n-1)
An-2A(n-1)=3×2^(n-2)
An/2^n-2A(n-1)/2^n=3×2^(n-2)/2^n
An/2^n-A(n-1)/2^(n-1)=3/4
A1/2^1=1/2
{An/2^n}是以1/2为首项,3/4为公差的等差数列
An/2^n=1/2+(n-1)3/4=(3n-1)/4
An=(3n-1)×2^(n-2)
设数列{an}的前n和为Sn,己知a1=1,Sn+1=4an+2,则{an}的通项公式为an=______.
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