Question

已知数列{a_n}满足a₁＝1，a_n＋1＝αa_n＋β，且a₂＝3，a₄＝15，求常数α，β的值．

Answer 1

答案：
解析：

由a1＝1，an＋1＝αan＋β知 a2＝αa1＋β即α＋β＝3                                                                                                                                                  ① a3＝αa2＋β＝3α＋β a4＝αa3＋β＝3α2＋αβ＋β 即3α2＋αβ＋β＝15                                                                                                                                                      ② 提示：