已知函数f(x)=2x+3,数列{an}满足a1=1,且a(n+1)=f(an)则该数列的通项公式an为?
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![已知函数f(x)=2x+3,数列{an}满足a1=1,且a(n+1)=f(an)则该数列的通项公式an为?](/uploads/image/z/3936234-66-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2x%2B3%2C%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E6%BB%A1%E8%B6%B3a1%3D1%2C%E4%B8%94a%28n%2B1%29%3Df%28an%29%E5%88%99%E8%AF%A5%E6%95%B0%E5%88%97%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fan%E4%B8%BA%3F)
已知函数f(x)=2x+3,数列{an}满足a1=1,且a(n+1)=f(an)则该数列的通项公式an为?
已知函数f(x)=2x+3,数列{an}满足a1=1,且a(n+1)=f(an)则该数列的通项公式an为?
已知函数f(x)=2x+3,数列{an}满足a1=1,且a(n+1)=f(an)则该数列的通项公式an为?
a(n+1)=2*an+3
即an=2*a(n-1)+3
an+3=2*a(n-1)+6=2[a(n-1)+3]
则{an+3}是公比q=2的等比数列
a1+3=4,
an+3=(a1+3)*q^(n-1)=4*2^(n-1)=2^(n+1)
an=2^(n+1)-3