数列[an],a1=5,an+1=2an+3,(n+1,n为下标),a9=?

问题描述:

数列[an],a1=5,an+1=2an+3,(n+1,n为下标),a9=?

a1=5
设a(n+1)+x=2(an+x)
则a(n+1)=2*an+x
则 x=3
则 a(n+1)+3=2(an+3)
则 (an+3)是以a1+3为首项 2为公比的等比数列
则 a9+3=(2^8)*(5+3)
a9=2045