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2001 AIME II Question 3

AIME · 2001 AIME II

Question 3

The first four terms are $x_1 = 211,$ $x_2 = 375,$ $x_3 = 420,$ and $x_4 = 523.$ For $n \ge 5,$ $$
\begin{aligned} x_n &= x_{n-1} - x_{n-2} \\ &\quad {}+ x_{n-3} - x_{n-4}. \end{aligned}
$$ Find the value of $x_{531} + x_{753} + x_{975}.$