a1=1,a(n+1)=3/2an+2,求an,要详解

来源：学生作业帮编辑：搜狗做题网作业帮分类：数学作业时间：2024/07/05 13:25:37

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
再问：你能帮忙化简一下吗？
再答：等比数列前n项和公式 Sn=[a1*(1-q^n)]/(1-q) a1=2 q=3/2 n=n-1 即 Sn=[2*(1-1.5^(n-1))]/-0.5 an=（3/2）^(n-1)+[2*(1-1.5^(n-1))]/-0.5

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