数列{an}中,a1=1,an-1=2an+3(n大于等于1),求该数列通式

题目

数列{an}中,a1=1,an-1=2an+3(n大于等于1),求该数列通式

答案

a(n-1)=2an+3
an = (1/2)a(n-1) - 3/2
an + 3 = (1/2)[ a(n-1) + 3]
=>{an + 3} 是等比数列, q=1/2
an + 3=(1/2)^(n-1).(a1 + 3)
=(1/2)^(n-1)
an =-3 +(1/2)^(n-1)