MathDB

8

Part of 1992 AIME Problems

Problems(1)

Sequence of Numbers

Source:

2/13/2006
For any sequence of real numbers A=(a1,a2,a3,…)A=(a_1,a_2,a_3,\ldots), define ΔA\Delta A to be the sequence (a2−a1,a3−a2,a4−a3,…)(a_2-a_1,a_3-a_2,a_4-a_3,\ldots), whose nthn^\text{th} term is an+1−ana_{n+1}-a_n. Suppose that all of the terms of the sequence Δ(ΔA)\Delta(\Delta A) are 11, and that a19=a92=0a_{19}=a_{92}=0. Find a1a_1.
quadraticsalgebrapolynomialAMCAIMEUSA(J)MOUSAMO