数列an满足sn=3an-1/2 计算a1,a2,a3,a4 猜an通项 求an前n项和sn

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数列an满足sn=3an-1/2 计算a1,a2,a3,a4 猜an通项 求an前n项和sn

数列an满足sn=3an-1/2 计算a1,a2,a3,a4 猜an通项 求an前n项和sn
数列an满足sn=3an-1/2 计算a1,a2,a3,a4 猜an通项 求an前n项和sn

数列an满足sn=3an-1/2 计算a1,a2,a3,a4 猜an通项 求an前n项和sn
a1=S1=3a1-1/2所以a1=1/4,依次可求出a2,a3,a4
求通项公式:Sn=3an-1/2①,Sn+1=3an+1-1/2②,②-①→an+1=3an+1-3an所以an+1/an=3/2所以{an}为公比q=3/2的等比数列,{an}的通项公式为:an=a1*q^n-1=1/4*3/2^n-1
a1,q知道了,Sn也就可以求出来了.

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