已知数列(an)满足an+1=2an+3×2∧n,a1=2求an

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已知数列(an)满足an+1=2an+3×2∧n,a1=2求an
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已知数列(an)满足an+1=2an+3×2∧n,a1=2求an
已知数列(an)满足an+1=2an+3×2∧n,a1=2求an

已知数列(an)满足an+1=2an+3×2∧n,a1=2求an

a(n+1)=2an+3·2ⁿ
等式两边同除以2ⁿ
a(n+1)/2ⁿ= an/2^(n-1) +3
a(n+1)/2ⁿ -an/2^(n-1)=3,为定值
a1/2^0=2/1=2,数列{an/2^(n-1)}是以2为首项,3为公差的等差数列
an/2^(n-1)=2+3(n-1)=3n-1
an=(3n-1)·2^(n-1)
数列{an}的通项公式为an=(3n-1)·2^(n-1)