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
问题描述:
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
答
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-1a1,q...