Question

已知等比数列{AN}的各项都是正数,且A2+A3=2+根号5,A3-A2=A1,求此数列的通向公式

Answer 1

A3-A2=A1,A1 ( q^2-q^1)=A1 ,q= (1+根5)/2

代入 A3+A2=2+根号5,解得 A1= (根5 -1) /2

An= (根5 -1) /2 * [(1+根5)/2]^(n-1) = [(1+根5)/2]^(n-2)

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