a(n+1)=an^2+6an+6=(an+3)^2-3,即a(n+1)+3=(an+3)^2，从而log5[a(n+1)+3]=2log5(an+3)而cn=log5(an+3),则结合上式即得c(n+1)=2cn，并且c1=1故{cn}为等比数列
