MathDB
Sequence

Source: 2006 AIME II 11

March 28, 2006
LaTeXAMCUSA(J)MOUSAMOAIMEgeometryAIME I

Problem Statement

A sequence is defined as follows a1=a2=a3=1a_1=a_2=a_3=1, and, for all positive integers nn, an+3=an+2+an+1+ana_{n+3}=a_{n+2}+a_{n+1}+a_n. Given that a28=6090307a_{28}=6090307, a29=11201821a_{29}=11201821, and a30=20603361a_{30}=20603361, find the remainder when ∑k=128ak\displaystyle \sum^{28}_{k=1} a_k is divided by 1000.
Back to ProblemsView on AoPS