a1=1,a(n+1)=3/2an+2,求an,要详解

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a1=1,a(n+1)=3/2an+2,求an,要详解
a1=1,a(n+1)=3/2an+2,求an,要详解

a1=1,a(n+1)=3/2an+2,求an,要详解
a1=1
a2=3/2a1+2
a3=3/2a2+2=（3/2）^2a1+2*(3/2)+2
a4=3/2a3+2=（3/2）^3a1+2*(3/2)^2+2*(3/2)+2
a5=（3/2）^4a1+2*(3/2)^3+2*(3/2)^2+2*(3/2)+2
……
an=（3/2）^(n-1)a1+2*(3/2)^（n-2）+……+2*(3/2)^3+2*(3/2)^2+2*(3/2)+2
把后边一部分用等比数列公式化简就行了

a(n+1)=1.5an+2
an=1.5a(n-1)+2
a(n+1)-an=1.5(an-a(n-1))
令a(n+1)-an=bn
a2-a1=b1=2.5
bn=1.5b(n-1)=1.5^2b(n-2)=1.5^(n-1)b1=2.5*1.5^(n-1)
a(n+1)-a1=2.5*(1.5^(n-1)+1.5^(n-2)+...+1)=5(1.5^n-1)
a(n+1)=5(1.5^n)-4
a(n)=5*(1.5^(n-1))-4

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