已知a1=3.an+1=2an+3,求an?

问题描述:

已知a1=3.an+1=2an+3,求an?

a(n+1)=2an+3 a(n+1)+k=2an+3+k=2(an+3/2+k/2) 则令k=3/2+k/2 k=3 则两边同时加3 a(n+1)+3=2(an+3) [a(n+1)+3]/(an+3)=2 所以an+3是等比数列,q=2 a1+3=6 所以an+3=6*2^(n-1) an=6*2^(n-1)-3