Question

已知数列{an}满足a1=2,a2=5,a4=23,且an+1=Aan+B,求实数A.B的取值.

Answer 1

a1=2,a2=5,a4=23

a2=Aa1+B

2A+B=5

B=5-2A

a3=Aa2+B=5A+B

a4=Aa3+B=A*(5A+B)+B=5A^2+AB+B=23

5A^2+A*(5-2A)+5-2A=23

3A^2+3A-18=0

A^2+A-6=0

(A+3)(A-2)=0

A1=-3

A2=2

A=-3

B=5+6=11

A=2

B=5-4=1