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x_{2010} =? if x_{n+1} =\frac{4 \max{x_n, 4}}{x_{n-1}}

Source: New Zealand NZMOC Camp Selection Problems 2010 Seniors 1

September 18, 2021
recurrence relationSequencealgebra

Problem Statement

For any two positive real numbers x0>0x_0 > 0, x1>0x_1 > 0, a sequence of real numbers is defined recursively by xn+1=4max⁡{xn,4}xn−1x_{n+1} =\frac{4 \max\{x_n, 4\}}{x_{n-1}} for n≥1n \ge 1. Find x2010x_{2010}.
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