数列AN满足A1=2,AN+1=AN^2+6AN+6,设CN=LOG5(AN+3),证{CN}为等比

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数列AN满足A1=2,AN+1=AN^2+6AN+6,设CN=LOG5(AN+3),证{CN}为等比

数列AN满足A1=2,AN+1=AN^2+6AN+6,设CN=LOG5(AN+3),证{CN}为等比
数列AN满足A1=2,AN+1=AN^2+6AN+6,设CN=LOG5(AN+3),证{CN}为等比

数列AN满足A1=2,AN+1=AN^2+6AN+6,设CN=LOG5(AN+3),证{CN}为等比
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