Number sequence

Procedure

Given \( a_{n+1} = k a_n + p a_{n-1} \), \( a_{n+1} - x a_n = (k - x) (a_n - x a_{n-1}) \) where \( x^2 = k x + p \)

Procedure: `y = x` Model

Baidu Scholar ixueshu

NCEE

数列 { \( a_n \) } 满足 \( a_1 = a \)， \( a_{n+1} = a_n^2 + a \) 且 \( \left\lvert a_n \right\rvert \leq 2 \)，则 \( a \) 的取值范围为（）

A. [-2,2] B. [-2,0] C. [0,\( \frac{1}{4} \)] D. [-2,\( \frac{1}{4}\)]

Scaling

\(a_1\frac{1-q^n}{1-q}\leq\frac{a_1}{1-q}\) where \(q\in(0,1)\)

NCEE