已知实数等比数列{an}， A3=1,且A4,A5+1,A6成等差数列

a3=aq^2=1

a4,a5+1,a6成等差数列
2(a*q^4+1)=a*q^3+a*q^5
2a*q^4+2=a*q^3+a*q^5
2q^2+2=q+q^3
q^3-2q^2+q-2=0
q^2(q-2)+q-2=0
(q-2)(q^2+1)=0 [q^2+1>0]
q=2

a3=a1q^2
1=a1*4
a1=1/4

an=1/4*2^n-1=2^n-3

a(n)=aq^(n-1),
1=a(3)=aq^2,
2[a(5)+1]=2[aq^4+1]=a(4)a(6)=[aq^3][aq^5]=a^2q^8,
2[aq^4+1]=2[aq^2*q^2+1]=2[q^2+1]=a^2q^8=(aq^2)^2*q^4=q^4,
0=q^4-2q^2-2,q^2=[2+(2^2+2*4)^(1/2)]/2=[2+(12)^(1/2)]/2=1+3^(1/2),
a=1/q^2=1/[1+3^(1/2)]=[3^(1/2)-1]/2,
q=[1+3^(1/2)]^(1/2)或q=-[1+3^(1/2)]^(1/2).

a(n)=([3^(1/2)-1]/2)[1+3^(1/2)]^[(n-1)/2]或
a(n)=([3^(1/2)-1]/2)[1+3^(1/2)]^[(n-1)/2](-1)^(n-1),
n=1,2,...

A6=q^3
A5+1=q^2+1
A4=q
q^3-（q^2+1）=q^2+1-q
q^3- 2q^2+q-2=0
（q-2）（q^2+1)=0
q=2
AN=q^(n-3)