MathDB

Sequence with Square Root

Source: AIME 2009II Problem 14

April 2, 2009

trigonometryinductionabsolute valueAMC

Problem Statement

The sequence

(a_n)

satisfies a_0 \equal{} 0 and \displaystyle a_{n \plus{} 1} \equal{} \frac85a_n \plus{} \frac65\sqrt {4^n \minus{} a_n^2} for

n\ge0

. Find the greatest integer less than or equal to

a_{10}